<?xml version="1.0" encoding="utf-8" standalone="yes"?><rss version="2.0" xmlns:atom="http://www.w3.org/2005/Atom" xmlns:content="http://purl.org/rss/1.0/modules/content/" xmlns:dc="http://purl.org/dc/elements/1.1/"><channel><title>Query-Planning on Opensource internals</title><link>https://articles.9j.nz/tags/query-planning/</link><description>Posts filed under Query-Planning on Opensource internals.</description><generator>Hugo</generator><language>en-US</language><managingEditor>Jay Hubbert</managingEditor><lastBuildDate>Wed, 21 Oct 2026 09:00:00 +0000</lastBuildDate><atom:link href="https://articles.9j.nz/tags/query-planning/index.xml" rel="self" type="application/rss+xml"/><item><title>ClickHouse Plans Distributed Queries with Cascades: A Real Cost-Based Optimizer</title><link>https://articles.9j.nz/posts/how-clickhouse-plans-distributed-queries-with-cascades/</link><pubDate>Wed, 21 Oct 2026 09:00:00 +0000</pubDate><dc:creator>Jay Hubbert</dc:creator><guid isPermaLink="true">https://articles.9j.nz/posts/how-clickhouse-plans-distributed-queries-with-cascades/</guid><category>clickhouse</category><category>performance</category><category>internals</category><category>query-planning</category><category>distributed</category><description>ClickHouse's experimental Cascades optimizer explores join strategies, aggregations and exchanges in a memo, then picks the cheapest with a three-dimensional cost model.</description><content:encoded>&lt;blockquote&gt;&#10;&lt;p&gt;&lt;strong&gt;TL;DR:&lt;/strong&gt; ClickHouse&amp;rsquo;s new Cascades optimizer treats a distributed query&#10;as a search problem. It generates alternative plans in a memo, prices each&#10;one with a work/network/sequential cost model, and ships the cheapest — but&#10;it refuses to guess, and fails loudly when it can&amp;rsquo;t decide.&lt;/p&gt;&#10;&lt;/blockquote&gt;&#10;&lt;p&gt;A single-node query plan has one obvious shape: read the table, filter,&#10;aggregate, sort. A distributed query does not.&lt;/p&gt;&#10;&lt;p&gt;The same &lt;code&gt;SELECT&lt;/code&gt; can be executed as a gather-everything-to-the-coordinator,&#10;or as a shuffle of both sides of a join followed by a local aggregation, or&#10;as a broadcast of a tiny dimension table to every node followed by a local&#10;join. And these choices &lt;em&gt;interact&lt;/em&gt; — the best join strategy depends on how&#10;the data will be aggregated afterwards, and the best aggregation strategy&#10;depends on how the join output is distributed.&lt;/p&gt;&#10;&lt;p&gt;So the planner has to explore combinations and compare them.&lt;/p&gt;&#10;&lt;p&gt;ClickHouse&amp;rsquo;s traditional answer was a set of fixed heuristics. Its new&#10;answer, arriving in 26.8 as an experimental setting, is a real cost-based&#10;optimizer built on the &lt;strong&gt;Cascades&lt;/strong&gt; framework: a memo of alternative plans, a&#10;set of rules that generate alternatives, and a cost model that prices them.&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Core/Settings.cpp:11131&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;DECLARE&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;Bool&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;enable_cascades_optimizer&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;R&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;(&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;Enable&lt;/span&gt; &lt;span class="n"&gt;the&lt;/span&gt; &lt;span class="n"&gt;Cascades&lt;/span&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;based&lt;/span&gt; &lt;span class="n"&gt;optimizer&lt;/span&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="n"&gt;distributed&lt;/span&gt; &lt;span class="n"&gt;query&lt;/span&gt; &lt;span class="n"&gt;plans&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;Takes&lt;/span&gt; &lt;span class="n"&gt;effect&lt;/span&gt; &lt;span class="n"&gt;only&lt;/span&gt; &lt;span class="n"&gt;together&lt;/span&gt; &lt;span class="n"&gt;with&lt;/span&gt; &lt;span class="err"&gt;`&lt;/span&gt;&lt;span class="n"&gt;make_distributed_plan&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="err"&gt;`&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;the&lt;/span&gt; &lt;span class="n"&gt;setting&lt;/span&gt; &lt;span class="n"&gt;alone&lt;/span&gt; &lt;span class="n"&gt;does&lt;/span&gt; &lt;span class="n"&gt;not&lt;/span&gt; &lt;span class="n"&gt;change&lt;/span&gt; &lt;span class="n"&gt;single&lt;/span&gt;&lt;span class="o"&gt;-&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt; &lt;span class="n"&gt;query&lt;/span&gt; &lt;span class="n"&gt;planning&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;, EXPERIMENTAL, \&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="s"&gt; {&amp;#34;&lt;/span&gt;&lt;span class="mf"&gt;26.8&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;, false, false, &amp;#34;&lt;/span&gt;&lt;span class="n"&gt;New&lt;/span&gt; &lt;span class="n"&gt;experimental&lt;/span&gt; &lt;span class="n"&gt;setting&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="s"&gt;&amp;#34;}) \&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;This article walks the implementation: the memo, the task-based search, the&#10;rules, the cost model, the enforcers, and the places where the&#10;implementation is deliberately conservative.&lt;/p&gt;&#10;&lt;h2 id="the-problem-the-optimizer-solves"&gt;The problem the optimizer solves&lt;/h2&gt;&#10;&lt;p&gt;The &lt;code&gt;ARCHITECTURE.md&lt;/code&gt; that ships with the code states it plainly:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;text&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-text" data-lang="text"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;## What Problem Does This Solve?&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;ClickHouse can execute a query on a single node using its standard pipeline: plan the&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;query, read from MergeTree, apply filters/expressions/joins/aggregations, return results.&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;But when data is spread across multiple nodes (shared storage like S3, or a multi-node&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;cluster), the optimizer must decide how to distribute the work:&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;- Should a join shuffle both sides by the join key, or broadcast the smaller table to&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; all nodes?&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;- Should an aggregation happen on each node first (partial agg) and then merge results,&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; or gather all data to one node and aggregate there?&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;- Should a table scan be split across N nodes (parallel read), or should each node read&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; the full table (replicated read for small dimension tables)?&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;- Where should exchanges (network data transfers between nodes) be placed?&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Pay attention to the third bullet. With shared storage (S3), a 25-row&#10;dimension table doesn&amp;rsquo;t need to be broadcast at all — every node can just&#10;read it from S3 itself.&lt;/p&gt;&#10;&lt;p&gt;That alternative, &lt;code&gt;ReplicatedRead&lt;/code&gt;, is exactly the kind of thing only a&#10;cost-based search would find, because it isn&amp;rsquo;t a &amp;ldquo;join strategy&amp;rdquo; in the&#10;classical sense. It&amp;rsquo;s a &lt;em&gt;read&lt;/em&gt; strategy, chosen because the cost of&#10;re-reading a tiny table is lower than the cost of shipping it.&lt;/p&gt;&#10;&lt;h2 id="the-memo"&gt;The memo&lt;/h2&gt;&#10;&lt;p&gt;The memo is the central data structure. It contains &lt;strong&gt;groups&lt;/strong&gt;, each&#10;representing a set of logically equivalent subexpressions. Each group holds&#10;both the &lt;em&gt;logical&lt;/em&gt; expressions (ways of computing the same thing) and the&#10;&lt;em&gt;physical&lt;/em&gt; expressions (ways of computing it with a concrete algorithm and&#10;concrete properties).&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Memo.h:10&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;Memo&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;public&lt;/span&gt;&lt;span class="o"&gt;:&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;explicit&lt;/span&gt; &lt;span class="n"&gt;Memo&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;LoggerPtr&lt;/span&gt; &lt;span class="n"&gt;log_&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="n"&gt;log&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;log_&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;GroupId&lt;/span&gt; &lt;span class="nf"&gt;addGroup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GroupExpressionPtr&lt;/span&gt; &lt;span class="n"&gt;group_expression&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;GroupPtr&lt;/span&gt; &lt;span class="nf"&gt;getGroup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GroupId&lt;/span&gt; &lt;span class="n"&gt;group_id&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;GroupConstPtr&lt;/span&gt; &lt;span class="nf"&gt;getGroup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GroupId&lt;/span&gt; &lt;span class="n"&gt;group_id&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="nf"&gt;getGroupCount&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;groups_by_id&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The plan is ingested into the memo one group per step. A step with children&#10;becomes a group whose expression has one &lt;em&gt;input link&lt;/em&gt; per child, and the&#10;input link carries the &lt;strong&gt;required properties&lt;/strong&gt; of that child:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Optimizer.cpp:179&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;group_expression&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;make_shared&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;GroupExpression&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;group_id&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;memo&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;addGroup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;group_expression&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="nl"&gt;child_node&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;children&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;input_group_id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;pending_props&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;addGroup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;child_node&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;group_expression&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="n"&gt;input_group_id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;pending_props&lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;So each input link carries the child&amp;rsquo;s group id &lt;em&gt;and&lt;/em&gt; the properties the&#10;parent requires of it. That&amp;rsquo;s where the &amp;ldquo;required properties&amp;rdquo; of the whole&#10;framework enter the picture.&lt;/p&gt;&#10;&lt;h3 id="properties-distribution-and-sorting"&gt;Properties: distribution and sorting&lt;/h3&gt;&#10;&lt;p&gt;A physical expression has two kinds of properties.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;Distribution&lt;/strong&gt; — how the data is spread over the nodes:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Properties.h:17&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;DistributionDescription&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;DistributionColumns&lt;/span&gt; &lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;/// Columns by which data is distributed. E.g. for shuffle exchange or partitioned table scan.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Type each key is cast to before hashing (parallel to `columns`; empty when the raw&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// types agree). Aligns buckets across both sides of a shuffle join.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Names&lt;/span&gt; &lt;span class="n"&gt;hash_type_names&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;is_replicated&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;/// All data is replicated to all nodes, so any distribution is satisfied. E.g. for small tables that are broadcasted to all nodes.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;node_count&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;/// Number of nodes among which data is distributed. E.g. for a shuffle exchange or a partitioned read.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="k"&gt;operator&lt;/span&gt;&lt;span class="o"&gt;==&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;DistributionDescription&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;other&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="k"&gt;default&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="nf"&gt;dump&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;WriteBuffer&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;out&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;String&lt;/span&gt; &lt;span class="nf"&gt;dump&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;};&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;&lt;strong&gt;Sorting&lt;/strong&gt; — whether the output is ordered, and by what.&lt;/p&gt;&#10;&lt;p&gt;A parent &lt;em&gt;requires&lt;/em&gt; properties of its child, and a child &lt;em&gt;satisfies&lt;/em&gt; a&#10;requirement if it provides at least as much. The matching isn&amp;rsquo;t trivial: a&#10;sorted-by-&lt;code&gt;(a)&lt;/code&gt; stream satisfies a requirement of &amp;ldquo;sorted by &lt;code&gt;(a)&lt;/code&gt;&amp;rdquo;, and the&#10;required sort must be a &lt;em&gt;prefix&lt;/em&gt; of the existing one:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Properties.cpp:9&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;ExpressionProperties&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;isSortingSatisfiedBy&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;SortDescription&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;required&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;SortDescription&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;existing&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Required sorting is satisfied by existing sorting if required is the prefix of existing&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;existing&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="n"&gt;i&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;required&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;existing&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;i&lt;/span&gt;&lt;span class="p"&gt;])&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;and the distribution match is &lt;em&gt;positional&lt;/em&gt; — data shuffled by &lt;code&gt;(b, a)&lt;/code&gt; does&#10;not colocate with data shuffled by &lt;code&gt;(a, b)&lt;/code&gt;:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Properties.cpp:39&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// The partition hash chains the key columns in order and may cast them first, so the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// match must be positional and the hash types must agree: data shuffled by `(b, a)`&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// or hashed at a different type does not colocate with data shuffled by `(a, b)`.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hash_type_names&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;existing&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hash_type_names&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;h3 id="sorting-is-a-property-not-an-operator"&gt;Sorting is a property, not an operator&lt;/h3&gt;&#10;&lt;p&gt;One design decision deserves a callout, because it differs from classical&#10;Cascades.&lt;/p&gt;&#10;&lt;p&gt;A plain &lt;code&gt;ORDER BY&lt;/code&gt; (no &lt;code&gt;LIMIT&lt;/code&gt;) is not an operator in the memo — it&amp;rsquo;s a&#10;&lt;em&gt;property&lt;/em&gt; that the parent requires of its input. The optimizer then&#10;produces the sort itself, if some child can provide it more cheaply:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Optimizer.cpp:162&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Strip a limit-less SortingStep::Full - pure sorting is a physical property, not a logical&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// one. Return the child&amp;#39;s GroupId along with the sorting as required properties, so the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// caller can attach them to the input link of the parent group expression.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// A SortingStep with a limit is a top-N (row-reducing) operator, so it is kept as an&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// operator instead; the limit is owned by that operator, never by the sorting property.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;sorting_step&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;typeid_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;SortingStep&lt;/span&gt; &lt;span class="o"&gt;*&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;sorting_step&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;sorting_step&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;getType&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;SortingStep&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Type&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Full&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;sorting_step&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;getLimit&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;chassert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;children&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;child_group_id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;_&lt;/span&gt;&lt;span class="p"&gt;]&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;addGroup&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;node&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;children&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;front&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;ExpressionProperties&lt;/span&gt; &lt;span class="n"&gt;stripped_props&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;stripped_props&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sorting&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;sorting_step&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;getSortDescription&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt;&lt;span class="n"&gt;child_group_id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;stripped_props&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;And a &lt;code&gt;LIMIT&lt;/code&gt; after the sort makes it a top-N, which reduces the row count&#10;and therefore &lt;em&gt;is&lt;/em&gt; an operator, with its own rules and its own cost.&lt;/p&gt;&#10;&lt;h2 id="the-search-tasks-on-a-stack"&gt;The search: tasks on a stack&lt;/h2&gt;&#10;&lt;p&gt;The optimizer is a LIFO stack of tasks. There are six task types, and a&#10;group moves through four stages.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;Stage 1 — Explore.&lt;/strong&gt; Transformation rules generate logically equivalent&#10;alternatives (join commutativity, two-stage aggregation).&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;Stage 2 — Implement.&lt;/strong&gt; Implementation rules turn logical expressions into&#10;physical ones with concrete properties (local join, broadcast join, shuffle&#10;join; local read, parallel read, replicated read).&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;Stage 3 — Enforce.&lt;/strong&gt; Enforcer rules bridge property gaps by inserting&#10;exchange steps.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;Stage 4 — Done.&lt;/strong&gt;&lt;/p&gt;&#10;&lt;p&gt;&lt;code&gt;OptimizeGroupTask&lt;/code&gt; drives the stages:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Task.cpp:38&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;isExplored&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Explore the group, then re-run `OptimizeGroupTask`&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;optimizer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pushTask&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;make_unique&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;OptimizeGroupTask&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;group_id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;optimizer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pushTask&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;make_unique&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;ExploreGroupTask&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;group_id&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;else&lt;/span&gt; &lt;span class="nf"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;isOptimizedFor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;optimizer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pushTask&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;make_unique&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;OptimizeGroupTask&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;group_id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="nl"&gt;expression&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;logical_expressions&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;optimizer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pushTask&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;make_unique&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;OptimizeExpressionTask&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;));&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;setOptimizedFor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The interesting part is the pruning decision at the top of the task, which&#10;is explicitly &lt;em&gt;not&lt;/em&gt; a cost-based prune:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Task.cpp:20&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Skip this group only if it is already fully processed (explored + implemented +&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// enforced) for these properties and has a satisfying plan - re-running would be a no-op.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// We deliberately do not prune just because a current best is within a finite cost budget:&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// the budget is an upper bound, not a lower bound, so such pruning is unsound for&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// optimality, and it can return before stage-3 enforcers add the distributed alternatives.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;cost_config&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;optimizer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;getMemo&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;getContext&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;cost_config&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;group_fully_processed&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;isExplored&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;isOptimizedFor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;isEnforcedFor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;group_fully_processed&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;getBestImplementation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;cost_config&lt;/span&gt;&lt;span class="p"&gt;).&lt;/span&gt;&lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;group&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;setFullyDoneFor&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;LOG_TEST&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;optimizer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;log&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="s"&gt;&amp;#34;OptimizeGroupTask group #{}: already fully processed&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;group_id&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;&lt;strong&gt;This is the part people get wrong&lt;/strong&gt; when they read this code.&lt;/p&gt;&#10;&lt;p&gt;Classical Cascades prunes with branch-and-bound: once a subtree&amp;rsquo;s cost&#10;exceeds the best complete plan, it gets dropped. ClickHouse&amp;rsquo;s implementation&#10;refuses to do that, because a subtree&amp;rsquo;s current best is an &lt;em&gt;upper&lt;/em&gt; bound on&#10;its final cost — a cheaper enforcer-built alternative may still appear — and&#10;pruning on it would be unsound.&lt;/p&gt;&#10;&lt;p&gt;Instead, the search is bounded by a task count.&lt;/p&gt;&#10;&lt;h3 id="rule-ordering"&gt;Rule ordering&lt;/h3&gt;&#10;&lt;p&gt;Every rule has a static &lt;em&gt;promise&lt;/em&gt; (a priority). The applicable rules are&#10;sorted by promise and pushed onto the LIFO stack, so the highest-promise&#10;rule runs first:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Task.cpp:169&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;pair&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Promise&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;OptimizationRulePtr&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&amp;gt;&lt;/span&gt; &lt;span class="n"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="nl"&gt;rule&lt;/span&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;rules&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;isApplied&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;rule&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;rule&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;checkPattern&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;optimizer&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;getMemo&lt;/span&gt;&lt;span class="p"&gt;()))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="n"&gt;rule&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;getPromise&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;rule&lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Sort ascending so the LIFO task stack pops the highest-promise rule first.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;sort&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;moves&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="p"&gt;[](&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="p"&gt;{&lt;/span&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;lhs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;first&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;rhs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;first&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="p"&gt;});&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The promise doesn&amp;rsquo;t change &lt;em&gt;which&lt;/em&gt; plans are considered — every applicable&#10;rule is eventually applied. It only changes the order, which breaks ties&#10;among equal-cost alternatives (the first-found best wins).&lt;/p&gt;&#10;&lt;h2 id="the-cost-model"&gt;The cost model&lt;/h2&gt;&#10;&lt;p&gt;The cost has three dimensions, combined by configurable weights:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Cost.h:39&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;struct&lt;/span&gt; &lt;span class="nc"&gt;CostConfig&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="n"&gt;work_weight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;/// Parallelizable work (scans, expression eval, I/O).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="n"&gt;network_weight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="c1"&gt;/// Per-byte network transfer.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Single-threaded phases (gather/scatter funnels, merge cursors). The weight is the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// per-node thread count: work parallelizes across the threads of a node while a serial&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// phase holds one thread, so one serial row costs about `threads` work rows (Brent&amp;#39;s law:&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// wall-clock ~ work / threads + serial path).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="n"&gt;sequential_weight&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;32.0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Fixed per-exchange latency (connection setup, metadata), in sequential rows. The&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// weighted value (~1e5 work units) keeps a plan over a small input local: distribution&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// cannot pay for its setup there.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="n"&gt;exchange_fixed_overhead&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mf"&gt;3000.0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;and the combination:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Cost.h:74&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="nf"&gt;total&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;CostConfig&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// If any component is infinite the plan is impossible; return infinity directly. Multiplying&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// first would let a zero weight turn `inf * 0` into NaN, and a NaN cost compares as neither&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// better nor worse, so an impossible plan could be picked as best.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;isfinite&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;work&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;isfinite&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;network&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;isfinite&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;sequential&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;numeric_limits&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;Float64&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;::&lt;/span&gt;&lt;span class="n"&gt;infinity&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;work&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;work_weight&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;network&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;network_weight&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;sequential&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sequential_weight&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The &lt;code&gt;inf * 0 = NaN&lt;/code&gt; guard is the kind of detail that separates a cost model&#10;that works from one that occasionally picks an impossible plan.&lt;/p&gt;&#10;&lt;h3 id="the-formulas"&gt;The formulas&lt;/h3&gt;&#10;&lt;p&gt;A hash join prices the probe, the output and the hash-table build:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Cost.cpp:130&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;Cost&lt;/span&gt; &lt;span class="nf"&gt;hashJoinCost&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;CostInputs&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;is_broadcast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;left_stats&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;inputStats&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;right_stats&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;inputStats&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Cost&lt;/span&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;work&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_row_count&lt;/span&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_row_count&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parallelism&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// The build side is materialized fully on every node for a broadcast join (the nodes build&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// concurrently) and 1/N per node otherwise. The build is work, not a sequential phase:&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// `parallel_hash` shards the hash table across threads within a node.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="n"&gt;build_rows_per_node&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;is_broadcast&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;?&lt;/span&gt; &lt;span class="n"&gt;right_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="nl"&gt;estimated_row_count&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;:&lt;/span&gt; &lt;span class="n"&gt;right_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_row_count&lt;/span&gt; &lt;span class="o"&gt;/&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;parallelism&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Hash table materialization: memory allocation + cache pressure.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;work&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hash_table_build_factor&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;build_rows_per_node&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;+&lt;/span&gt; &lt;span class="n"&gt;build_rows_per_node&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;right_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_bytes_per_row&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The &lt;em&gt;exchange&lt;/em&gt; prices the network, and the distinction between a shuffle and&#10;a gather is where most of the distributed reasoning lives:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Cost.cpp:240&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;Cost&lt;/span&gt; &lt;span class="nf"&gt;exchangeCost&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;CostInputs&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;IQueryPlanStep&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// A sorted gather over a partial top-N transfers min(input_rows, L * node_count) rows,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// not the group&amp;#39;s trimmed L; the caller resolves that override from the memo.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;exchange_rows_override&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;value_or&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_row_count&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Cost&lt;/span&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// The network term is wall-clock per node, like the work term. A shuffle (N-&amp;gt;N) moves&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// 1/N of the data per node, all nodes concurrently; without the division one node&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// scanning the whole table is priced the same as the cluster shuffling it, and the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// optimizer keeps big scans on a single node.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Float64&lt;/span&gt; &lt;span class="n"&gt;network_bytes&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_bytes_per_row&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;dynamic_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;ShuffleExchangeStep&lt;/span&gt; &lt;span class="o"&gt;*&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;network_bytes&lt;/span&gt; &lt;span class="o"&gt;/=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;max&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="mf"&gt;1.0&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;node_count&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;network&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;network_bytes&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sequential&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;exchange_fixed_overhead&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Gather (N-&amp;gt;1) and Scatter (1-&amp;gt;N) funnel every row through a single node that&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// sends or receives them sequentially, so their transfer stays undivided and each row&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// pays the funnel cost. Without it a gather of a large input looks as cheap as a&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// shuffle, so the optimizer distributes work (e.g. a sort) that should stay local.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;dynamic_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;GatherExchangeStep&lt;/span&gt; &lt;span class="o"&gt;*&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="k"&gt;dynamic_cast&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;ScatterExchangeStep&lt;/span&gt; &lt;span class="o"&gt;*&amp;gt;&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sequential&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;funnel_sequential_cost_per_row&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;rows&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Three subtleties are worth spelling out:&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;A &lt;strong&gt;shuffle&lt;/strong&gt; divides the network cost by the node count, because each node&#10;ships 1/N of the data and all nodes do it concurrently.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;A &lt;strong&gt;broadcast&lt;/strong&gt; does &lt;em&gt;not&lt;/em&gt; divide, because every node ingests the whole&#10;payload:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Cost.cpp:227&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;Cost&lt;/span&gt; &lt;span class="nf"&gt;broadcastExchangeCost&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;CostInputs&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;Cost&lt;/span&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// The network term is wall-clock per node, like the work term (which is divided by&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// parallelism): every receiving node ingests the full payload, all of them concurrently,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// and the senders each ship their share of the copies in parallel. So one full payload&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// is the per-node bound. A shuffle moves 1/N per node, so a broadcast still costs N times&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// a shuffle of the same data.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;network&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_row_count&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_bytes_per_row&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sequential&lt;/span&gt; &lt;span class="o"&gt;+=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;config&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;exchange_fixed_overhead&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;/li&gt;&#10;&lt;li&gt;&#10;&lt;p&gt;Every exchange pays a &lt;strong&gt;fixed overhead&lt;/strong&gt; in sequential units, which is what&#10;keeps a plan over a small input local: distributing 25 rows is not worth a&#10;network round trip.&lt;/p&gt;&#10;&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;h3 id="a-read-is-priced-on-its-scan-volume-not-its-output"&gt;A read is priced on its scan volume, not its output&lt;/h3&gt;&#10;&lt;p&gt;This one is subtle and important. A filter that the primary key can&amp;rsquo;t prune&#10;leaves the whole granule selection to scan, so the &lt;em&gt;output&lt;/em&gt; estimate badly&#10;understates the cost:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Cost.cpp:150&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// One node reads the whole table.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;static&lt;/span&gt; &lt;span class="n"&gt;Cost&lt;/span&gt; &lt;span class="nf"&gt;fullReadCost&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;CostInputs&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Price the scan volume, not the output volume: a filter the primary key cannot prune&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// leaves the whole granule selection to scan, and without this a replicated read of such&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// a table would look orders of magnitude cheaper than the scan it does.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;physical_read_bytes&lt;/span&gt; &lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;Cost&lt;/span&gt;&lt;span class="p"&gt;{.&lt;/span&gt;&lt;span class="n"&gt;work&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;physical_read_bytes&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;Cost&lt;/span&gt;&lt;span class="p"&gt;{.&lt;/span&gt;&lt;span class="n"&gt;work&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_row_count&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;inputs&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;output_stats&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;estimated_bytes_per_row&lt;/span&gt;&lt;span class="p"&gt;};&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Without this, &lt;code&gt;ReplicatedRead&lt;/code&gt; — every node reading the whole table from S3&#10;— would look free for a table whose filter prunes 99 % of the rows.&lt;/p&gt;&#10;&lt;h3 id="the-cost-model-is-query-tunable"&gt;The cost model is query-tunable&lt;/h3&gt;&#10;&lt;p&gt;Everything above is overridable with one JSON parameter:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;sql&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-sql" data-lang="sql"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;SET&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;param__internal_cascades_cost_config&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s1"&gt;&amp;#39;{&amp;#34;work_weight&amp;#34;:1,&amp;#34;network_weight&amp;#34;:1,&amp;#34;sequential_weight&amp;#34;:32}&amp;#39;&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;and an invalid configuration rejects the query rather than silently falling&#10;back to the defaults.&lt;/p&gt;&#10;&lt;h2 id="the-rules"&gt;The rules&lt;/h2&gt;&#10;&lt;h3 id="join-implementations"&gt;Join implementations&lt;/h3&gt;&#10;&lt;p&gt;One rule produces all the join alternatives:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/HashJoinImplementation.cpp:19&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// Produces all applicable hash join implementations in a single rule:&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// - Local join: both inputs gathered to one node (always applicable)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// - Broadcast join: left partitioned any way, right replicated (only when node_count &amp;gt; 1)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// - Partitioned (shuffle) join: both inputs shuffled by join keys (only when node_count &amp;gt; 1&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// and the join has equi-join predicates)&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;///&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// When node_count == 1 all three strategies produce the same plan, so only the local join&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// is emitted to avoid redundant identical alternatives in the memo.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;HashJoinImplementation&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="k"&gt;public&lt;/span&gt; &lt;span class="n"&gt;IOptimizationRule&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;A shuffle join partitions both sides by the join key. The key columns are&#10;recorded &lt;em&gt;positionally&lt;/em&gt; on both sides, together with the type they&amp;rsquo;re hashed&#10;at:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/HashJoinImplementation.cpp:316&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;add_key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="o"&gt;&amp;amp;&lt;/span&gt;&lt;span class="p"&gt;](&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;JoinKeyPair&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;left_dist&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;right_dist&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;({&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;});&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;needs_hash_cast&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;String&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;type_name&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;hash_type_for&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;left_dist&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hash_type_names&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;type_name&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;right_dist&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hash_type_names&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;push_back&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;type_name&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Advertise the output partitioning only on the preserved side(s).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;NameSet&lt;/span&gt; &lt;span class="n"&gt;output_key&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;left_preserved&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;output_key&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;left&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;right_preserved&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;output_key&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;insert&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;right&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The &lt;code&gt;hash_type_names&lt;/code&gt; exist because if the two sides have different key&#10;types, they must be cast to a common type &lt;em&gt;before&lt;/em&gt; hashing. Otherwise the&#10;two sides land in different buckets and the join produces nothing.&lt;/p&gt;&#10;&lt;h3 id="two-stage-aggregation"&gt;Two-stage aggregation&lt;/h3&gt;&#10;&lt;p&gt;The transformation rule splits a single-phase aggregation into a partial and&#10;a merge:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/AggregationImplementations.cpp:92&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// Logical transformation that splits a single-phase Agg into a two-phase plan:&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// PartialAgg(input) -&amp;gt; ShuffleExchange -&amp;gt; FinalMergeAgg&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;///&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// PartialAgg computes partial aggregate states locally on each node without finalization.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// FinalMergeAgg receives pre-aggregated states and merges them into final results.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// The exchange between the two is inserted by the `DistributionEnforcer` based on the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// distribution requirements set by the implementation rules on FinalMergeAgg.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;///&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// A non-final aggregation is split too when it promises bucket order to a consumer outside the&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// plan: the merge then stays non-final and restores the bucket order over the gathered partials,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// which is the distributed alternative to the single-node partial `AggregationImplementation`&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// leaves for such a step.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;TwoStageAggregationTransformation&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="k"&gt;public&lt;/span&gt; &lt;span class="n"&gt;IOptimizationRule&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;and the split clones the aggregation step, marks the clone as non-final, and&#10;creates a &lt;code&gt;MergingAggregatedStep&lt;/code&gt; for the merge half:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/AggregationImplementations.cpp:345&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Phase 1: partial aggregation - takes raw rows, outputs intermediate aggregate states.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;partial_step_ptr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;cloneStepAs&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;agg_step&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;*&lt;/span&gt; &lt;span class="n"&gt;partial_step&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;partial_step_ptr&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;get&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;partial_step&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;setFinal&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The shuffle aggregation is only applicable in some cases, and every one of&#10;those reasons is a correctness reason:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/AggregationImplementations.cpp:64&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// See `addShuffleAggregation` for why each condition disables the shuffle strategy.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="nf"&gt;isShuffleApplicable&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;agg_step&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;getParams&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;keys&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;agg_step&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;isGroupingSets&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;agg_step&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;getParams&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;overflow_row&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;agg_step&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;getParams&lt;/span&gt;&lt;span class="p"&gt;().&lt;/span&gt;&lt;span class="n"&gt;max_rows_to_group_by&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;no group keys → a global aggregation has nothing to shuffle by;&lt;/li&gt;&#10;&lt;li&gt;grouping sets → the keys are the &lt;em&gt;union&lt;/em&gt; of the sets&amp;rsquo; keys, so shuffling&#10;by the union splits the rows of one grouping-set group across nodes;&lt;/li&gt;&#10;&lt;li&gt;an overflow row → every node would emit its own;&lt;/li&gt;&#10;&lt;li&gt;&lt;code&gt;max_rows_to_group_by&lt;/code&gt; → the limit is a global contract, but each node&#10;would enforce it independently.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;h3 id="single-key-shuffle-alternatives"&gt;Single-key shuffle alternatives&lt;/h3&gt;&#10;&lt;p&gt;A nice touch: for a multi-key &lt;code&gt;GROUP BY&lt;/code&gt;, the optimizer also considers&#10;shuffling by &lt;em&gt;one&lt;/em&gt; of the keys, which is cheaper (fewer bytes in the&#10;exchange) and still correct:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/AggregationImplementations.cpp:198&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// Single-key shuffle alternatives.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// For aggregations with 2+ group-by keys, generate a shuffle alternative for each&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// individual key. Correctness: `GROUP BY (A, B)` with data shuffled by `A` is correct&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// because all rows with the same `(A, B)` have the same `A`, hence the same node.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="n"&gt;AggregationImplementation&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;StrategyEnumerator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;addSingleKeyShuffleAggregations&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;vector&lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="n"&gt;size_t&lt;/span&gt;&lt;span class="o"&gt;&amp;gt;&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;candidate_node_counts&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;h2 id="enforcers-self-referential-expressions"&gt;Enforcers: self-referential expressions&lt;/h2&gt;&#10;&lt;p&gt;When a parent requires &lt;code&gt;{1 node}&lt;/code&gt; and the cheapest child produces&#10;&lt;code&gt;{4 nodes}&lt;/code&gt;, something has to bridge the gap. That something is an&#10;&lt;em&gt;enforcer&lt;/em&gt; — an exchange step inserted by the optimizer.&lt;/p&gt;&#10;&lt;p&gt;Enforcers are the hairiest part of the implementation, because an enforcer&amp;rsquo;s&#10;input is the &lt;em&gt;same group&lt;/em&gt; with relaxed requirements. That looks like a cycle:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/DistributionEnforcer.cpp:24&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// Produces self-referential enforcer expressions that bridge distribution gaps.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// Each enforcer expression lives in the same group as the source expression; its&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// single input points back to the same group with normalized properties (node_count,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// is_replicated, and sorting where needed) as the requirement - this lets the optimizer&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// pick the cheapest source with that distribution shape. The optimizer recursively&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// satisfies this self-referential input through the normal task mechanism, enabling&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// natural enforcer composition (e.g. a sort and a gather compose into gather-then-sort,&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// see `SortingEnforcer`, without&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;/// bundling steps).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;class&lt;/span&gt; &lt;span class="nc"&gt;DistributionEnforcer&lt;/span&gt; &lt;span class="o"&gt;:&lt;/span&gt; &lt;span class="k"&gt;public&lt;/span&gt; &lt;span class="n"&gt;IOptimizationRule&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The construction is centralised:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Rules/DistributionEnforcer.cpp:104&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="n"&gt;DistributionEnforcer&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;EnforcerEnumerator&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;addEnforcer&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;QueryPlanStepPtr&lt;/span&gt; &lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;ExpressionProperties&lt;/span&gt; &lt;span class="n"&gt;input_required&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;SortDescription&lt;/span&gt; &lt;span class="n"&gt;output_sorting&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;ExpressionProperties&lt;/span&gt; &lt;span class="n"&gt;output_properties&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;output_properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;distribution&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;distribution&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;output_properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sorting&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;output_sorting&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;enforcer_expr&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;makeEnforcerExpression&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;step&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input_required&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;output_properties&lt;/span&gt;&lt;span class="p"&gt;),&lt;/span&gt; &lt;span class="n"&gt;EnforcedProperty&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Distribution&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;rule&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;addPhysicalToMemo&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;enforcer_expr&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;memo&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;result&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;Two invariants keep the self-reference acyclic.&lt;/p&gt;&#10;&lt;p&gt;The first is that an enforcer carries an &lt;em&gt;axis&lt;/em&gt; (&lt;code&gt;Sorting&lt;/code&gt; or &lt;code&gt;Distribution&lt;/code&gt;),&#10;and an enforcer that satisfies a wildcard axis only by over-providing on it&#10;isn&amp;rsquo;t eligible. A sorted enforcer can&amp;rsquo;t fill an empty-sort slot; a keyed&#10;exchange can&amp;rsquo;t fill an empty-columns slot:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Group.cpp:159&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;input_is_self_referential&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;enforced_property&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;EnforcedProperty&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;None&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Empty sort requirement: reject a sorted enforcer (it over-provides on the sort axis).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sorting&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;sorting&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Empty distribution-columns requirement: reject a keyed exchange. A sorting enforcer&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// carrying keyed columns is still needed to feed a sorted gather, so keep it eligible.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;enforced_property&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;EnforcedProperty&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;Distribution&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;required_properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;distribution&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;distribution&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;columns&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;||&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;distribution&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;hash_type_names&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;()))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The second is that an enforcer must never evict a non-enforcer alternative&#10;from the best-implementation cache, because that alternative is the acyclic&#10;way out:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Group.cpp:78&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// An enforcer &amp;#34;satisfies&amp;#34; a weaker non-enforcer only by over-providing (e.g. a sorted gather&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// covers an empty-sort requirement). Dropping the base would leave a self-referential enforcer&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// chain with no acyclic alternative, so an enforcer never suppresses or evicts a distinct base.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;enforcer_over_provides_for&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="p"&gt;[](&lt;/span&gt;&lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;GroupExpressionPtr&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;enforcer_candidate&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;GroupExpressionPtr&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;base_candidate&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt; &lt;span class="n"&gt;enforcer_candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;enforced_property&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;EnforcedProperty&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;None&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;base_candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;enforced_property&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;EnforcedProperty&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;None&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;enforcer_candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt; &lt;span class="o"&gt;==&lt;/span&gt; &lt;span class="n"&gt;base_candidate&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;};&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;h3 id="the-fixed-point"&gt;The fixed point&lt;/h3&gt;&#10;&lt;p&gt;Enforcers compose: a sort enables a sorted gather, which enables a gather. The&#10;Stage 3 loop iterates until no new enforcer is produced:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Task.cpp:96&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Fixed-point loop: iterate over newly-added physical expressions until no&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// new enforcers are produced. Each iteration may create expressions that&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// enable further enforcers (e.g. a sort enables a sorted `GatherExchange`).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;enforced_up_to&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="kt"&gt;bool&lt;/span&gt; &lt;span class="n"&gt;new_enforcers_created&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;true&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;while&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;new_enforcers_created&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;new_enforcers_created&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="nb"&gt;false&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;h2 id="keeping-the-best-implementation"&gt;Keeping the best implementation&lt;/h2&gt;&#10;&lt;p&gt;Each group keeps a Pareto frontier of implementations, bucketed by&#10;distribution shape so that a lookup is O(1) plus a short scan:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Group.cpp:73&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="kt"&gt;void&lt;/span&gt; &lt;span class="n"&gt;Group&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;updateBestImplementation&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;GroupExpressionPtr&lt;/span&gt; &lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;CostConfig&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;cost_config&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;UInt64&lt;/span&gt; &lt;span class="n"&gt;key&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;distributionKey&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;distribution&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;bucket&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;best_implementations&lt;/span&gt;&lt;span class="p"&gt;[&lt;/span&gt;&lt;span class="n"&gt;key&lt;/span&gt;&lt;span class="p"&gt;];&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;and the eviction rule is a domination test: an implementation is dropped when&#10;another one satisfies at least the same properties at a lower cost.&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Group.cpp:88&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Remove all known best expressions with higher cost and properties satisfied by the new expression.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Only the matching distribution-shape bucket needs checking - `isSatisfiedBy` requires&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// exact match on (node_count, is_replicated).&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;best_it&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;bucket&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;begin&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt; &lt;span class="n"&gt;best_it&lt;/span&gt; &lt;span class="o"&gt;!=&lt;/span&gt; &lt;span class="n"&gt;bucket&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;end&lt;/span&gt;&lt;span class="p"&gt;();)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;isSatisfiedBy&lt;/span&gt;&lt;span class="p"&gt;((&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;best_it&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;properties&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;best_it&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;subtree_cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;total&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cost_config&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;=&lt;/span&gt; &lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;cost&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;subtree_cost&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;total&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;cost_config&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;enforcer_over_provides_for&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="n"&gt;best_it&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;expression&lt;/span&gt;&lt;span class="p"&gt;))&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// There is already a cheaper implementation that satisfies the same properties&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;return&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;h2 id="failing-closed"&gt;Failing closed&lt;/h2&gt;&#10;&lt;p&gt;The search is bounded by a task count, not by branch-and-bound. And when the&#10;budget runs out, the query is &lt;em&gt;rejected&lt;/em&gt; rather than planned from a partial&#10;memo:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Optimizer.cpp:308&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Limit the time in terms of optimization tasks instead of wall clock time. This is done for stability of generated plans regardless of system load.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Microsoft SQL Server&amp;#39;s optimizer team describes this in Andy Pavlo&amp;#39;s seminar: https://www.youtube.com/watch?v=pQe1LQJiXN0&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;const&lt;/span&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;executed_tasks_limit&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;getCascadesTaskLimitParam&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;query_context&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;CascadesDefaults&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;DEFAULT_TASK_LIMIT&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;executed_tasks_count&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;0&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;for&lt;/span&gt; &lt;span class="p"&gt;(;&lt;/span&gt; &lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt; &lt;span class="o"&gt;&amp;amp;&amp;amp;&lt;/span&gt; &lt;span class="n"&gt;executed_tasks_count&lt;/span&gt; &lt;span class="o"&gt;&amp;lt;&lt;/span&gt; &lt;span class="n"&gt;executed_tasks_limit&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt; &lt;span class="o"&gt;++&lt;/span&gt;&lt;span class="n"&gt;executed_tasks_count&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;{&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;auto&lt;/span&gt; &lt;span class="n"&gt;task&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="n"&gt;std&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;move&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;pop&lt;/span&gt;&lt;span class="p"&gt;();&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;task&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;execute&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;*&lt;/span&gt;&lt;span class="k"&gt;this&lt;/span&gt;&lt;span class="p"&gt;);&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="p"&gt;}&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/Optimizer.cpp:321&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Fail closed if the search did not finish within the task budget: building a plan from a&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// partial memo can yield a non-minimal plan or a confusing failure deep inside buildBestPlan.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="c1"&gt;/// Surface a clear error instead and point at the knob to raise the limit.&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;if&lt;/span&gt; &lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="o"&gt;!&lt;/span&gt;&lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;empty&lt;/span&gt;&lt;span class="p"&gt;())&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="k"&gt;throw&lt;/span&gt; &lt;span class="n"&gt;Exception&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;ErrorCodes&lt;/span&gt;&lt;span class="o"&gt;::&lt;/span&gt;&lt;span class="n"&gt;SUPPORT_IS_DISABLED&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;Cascades optimizer did not finish within the task budget of {} tasks &amp;#34;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;(root group #{}, required properties {}, {} groups in memo, {} tasks left, next: {}). &amp;#34;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;The distributed Cascades optimizer is experimental; set enable_cascades_optimizer = 0 &amp;#34;&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="s"&gt;&amp;#34;or simplify the query.&amp;#34;&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;executed_tasks_limit&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root_group_id&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt; &lt;span class="n"&gt;root_required_properties&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;dump&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt; &lt;span class="n"&gt;memo&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;getGroupCount&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;size&lt;/span&gt;&lt;span class="p"&gt;(),&lt;/span&gt; &lt;span class="n"&gt;tasks&lt;/span&gt;&lt;span class="p"&gt;.&lt;/span&gt;&lt;span class="n"&gt;top&lt;/span&gt;&lt;span class="p"&gt;()&lt;/span&gt;&lt;span class="o"&gt;-&amp;gt;&lt;/span&gt;&lt;span class="n"&gt;describe&lt;/span&gt;&lt;span class="p"&gt;());&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The default budget is 100 000 tasks:&lt;/p&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;cpp&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-cpp" data-lang="cpp"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="c1"&gt;// src/Processors/QueryPlan/Optimizations/Cascades/OptimizerDefaults.h:17&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;constexpr&lt;/span&gt; &lt;span class="n"&gt;size_t&lt;/span&gt; &lt;span class="n"&gt;DEFAULT_TASK_LIMIT&lt;/span&gt; &lt;span class="o"&gt;=&lt;/span&gt; &lt;span class="mi"&gt;100000&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;h2 id="trying-it"&gt;Trying it&lt;/h2&gt;&#10;&lt;div class="code-block"&gt;&#10; &lt;div class="code-block-head"&gt;&#10; &lt;span class="code-lang"&gt;sql&lt;/span&gt;&#10; &lt;button class="code-copy" type="button" data-copy&gt;Copy&lt;/button&gt;&#10; &lt;/div&gt;&#10; &lt;div class="code-block-body"&gt;&#10; &lt;div class="highlight"&gt;&lt;pre tabindex="0" class="chroma"&gt;&lt;code class="language-sql" data-lang="sql"&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;SET&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;enable_cascades_optimizer&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;SET&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;make_distributed_plan&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="mi"&gt;1&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;SELECT&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;n_name&lt;/span&gt;&lt;span class="p"&gt;,&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;SUM&lt;/span&gt;&lt;span class="p"&gt;(&lt;/span&gt;&lt;span class="n"&gt;o_totalprice&lt;/span&gt;&lt;span class="p"&gt;)&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;revenue&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;FROM&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;orders&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;customer&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;o_custkey&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;c_custkey&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;JOIN&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;nation&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;ON&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;c_nationkey&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;n_nationkey&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;WHERE&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;o_orderdate&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s1"&gt;&amp;#39;1995-01-01&amp;#39;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;AND&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;o_orderdate&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;&amp;lt;&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s1"&gt;&amp;#39;1995-04-01&amp;#39;&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;GROUP&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;BY&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;n_name&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="k"&gt;ORDER&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;BY&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;revenue&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="k"&gt;DESC&lt;/span&gt;&lt;span class="w"&gt;&#10;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;span class="line"&gt;&lt;span class="cl"&gt;&lt;span class="n"&gt;SETTINGS&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="n"&gt;send_logs_level&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="o"&gt;=&lt;/span&gt;&lt;span class="w"&gt; &lt;/span&gt;&lt;span class="s1"&gt;&amp;#39;test&amp;#39;&lt;/span&gt;&lt;span class="p"&gt;;&lt;/span&gt;&lt;/span&gt;&lt;/span&gt;&lt;/code&gt;&lt;/pre&gt;&lt;/div&gt;&#10; &lt;/div&gt;&#10;&lt;/div&gt;&#10;&lt;p&gt;The &lt;code&gt;test&lt;/code&gt; log level prints the memo, every costed expression with its&#10;work/network/sequential breakdown, and the final plan — which is the&#10;intended way to understand &lt;em&gt;why&lt;/em&gt; the optimizer chose what it chose.&lt;/p&gt;&#10;&lt;h2 id="trade-offs"&gt;Trade-offs&lt;/h2&gt;&#10;&lt;p&gt;&lt;strong&gt;What it buys:&lt;/strong&gt; plans that no fixed heuristic would produce. A broadcast of&#10;a tiny table instead of a shuffle of a huge one. A &lt;code&gt;ReplicatedRead&lt;/code&gt; from&#10;shared storage instead of a network transfer. A two-phase aggregation instead&#10;of a gather. A sort per node instead of a sort of everything.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;What it costs:&lt;/strong&gt;&lt;/p&gt;&#10;&lt;ul&gt;&#10;&lt;li&gt;&lt;strong&gt;It is experimental.&lt;/strong&gt; The setting is &lt;code&gt;EXPERIMENTAL&lt;/code&gt; and off by default,&#10;and it only applies with &lt;code&gt;make_distributed_plan = 1&lt;/code&gt;.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Join ordering is &lt;em&gt;not&lt;/em&gt; part of it.&lt;/strong&gt; This is the biggest difference from&#10;classical Cascades. ClickHouse fixes the join order first (with the&#10;existing &lt;code&gt;dpsize&lt;/code&gt;/&lt;code&gt;dphyp&lt;/code&gt;/&lt;code&gt;greedy&lt;/code&gt; algorithms) and Cascades only optimises&#10;the &lt;em&gt;distribution&lt;/em&gt; strategy. The published literature calls this the &amp;ldquo;split&amp;rdquo;&#10;design, and it loses the global optimum when the join order interacts with&#10;physical properties — which, in a distributed setting, it does.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;The statistics are weak.&lt;/strong&gt; Today they come from index analysis and from&#10;query-parameter hints. There&amp;rsquo;s no cardinality estimator as sophisticated as&#10;the one the pre-Cascades join orderer uses. A cost model on bad statistics&#10;picks the wrong plan confidently.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Only two parallelism levels are explored&lt;/strong&gt;: &lt;code&gt;{1 node}&lt;/code&gt; and &lt;code&gt;{N nodes}&lt;/code&gt;.&#10;Intermediate counts were never chosen on TPC-H, and exploring them would&#10;multiply the search space.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;The search can be exponential&lt;/strong&gt;, which is why there&amp;rsquo;s a hard task budget&#10;and a fail-closed error. Classical Cascades would prune instead.&lt;/li&gt;&#10;&lt;li&gt;&lt;strong&gt;Some plan shapes are rejected outright&lt;/strong&gt; — &lt;code&gt;WITH TOTALS&lt;/code&gt;, &lt;code&gt;ROLLUP&lt;/code&gt;,&#10;&lt;code&gt;CUBE&lt;/code&gt;, extremes, &lt;code&gt;PASTE JOIN&lt;/code&gt;, and reads that cannot be cloned across&#10;workers.&lt;/li&gt;&#10;&lt;/ul&gt;&#10;&lt;h2 id="wrapping-up"&gt;Wrapping up&lt;/h2&gt;&#10;&lt;p&gt;&lt;strong&gt;Here&amp;rsquo;s the thing:&lt;/strong&gt; the most interesting part of this code isn&amp;rsquo;t the&#10;optimizer. It&amp;rsquo;s the &lt;em&gt;discipline&lt;/em&gt; around it.&lt;/p&gt;&#10;&lt;p&gt;Every place where the implementation deliberately deviates from the textbook&#10;— no branch-and-bound, a fail-closed budget, the enforcer-axis rules, the&#10;&amp;ldquo;never evict the acyclic fallback&amp;rdquo; rule — carries a comment explaining&#10;exactly why the textbook version would be wrong here. That&amp;rsquo;s rare, and it&amp;rsquo;s&#10;the part of the code most worth reading.&lt;/p&gt;&#10;&lt;p&gt;&lt;strong&gt;What to do about it:&lt;/strong&gt; if you&amp;rsquo;re running a distributed ClickHouse cluster,&#10;turn &lt;code&gt;enable_cascades_optimizer = 1&lt;/code&gt; on a staging cluster, set&#10;&lt;code&gt;send_logs_level = 'test'&lt;/code&gt;, and read the memo for one of your real queries.&#10;You&amp;rsquo;ll see immediately whether your statistics are good enough for it to&#10;trust itself.&lt;/p&gt;&#10;&lt;p&gt;And if you hit the task budget, that&amp;rsquo;s not a bug — that&amp;rsquo;s the optimizer&#10;telling you it couldn&amp;rsquo;t afford to think. Fix the query shape, or raise the&#10;limit.&lt;/p&gt;&#10;</content:encoded></item></channel></rss>