数据库内核月报

MySQL JOIN简介

MySQL本身没有常规意义上的执行计划，一般情况就是通过JOIN和QEP_TAB这两个结构组成。QEP_TAB 的全称是Query Execution Plan Table，这个“Table“可以是物理表、内存表、常量表、子查询的结果表等等。作为整个单独JOIN执行计划载体之前还承担着整个执行路径的调用和流转，但是从8.0.20后，全面的生成了独立的Iterator执行器引擎模式。在8.0.22中，又引入了AccessPath概念，真正的生成了独立的执行计划，从而进一步做到了优化过程到树型执行计划，最后到Iterator载体在执行引擎中的执行。

MySQL原始的Join都是依赖于QEP_TAB列表，因为原来MySQL并不支持其他形态的Join结构，只支持左深树，那很容易直接使用数组来表示就可以了。优化器在生成执行计划只需要在QEP_TAB上增加JOIN的属性op_type，就可以递归去使用不同的Join方法和表访问方式了。

  // Operation between the previous QEP_TAB and this one.
  enum enum_op_type {
    // Regular nested loop.
    OT_NONE,

    // Aggregate (GROUP BY).
    OT_AGGREGATE,

    // Various temporary table operations, used at the end of the join.
    OT_MATERIALIZE,
    OT_AGGREGATE_THEN_MATERIALIZE,
    OT_AGGREGATE_INTO_TMP_TABLE,
    OT_WINDOWING_FUNCTION,

    // Block-nested loop (rewritten to hash join).
    OT_BNL,

    // Batch key access.
    OT_BKA
  } op_type = OT_NONE;

Hypergraph Join Optimizer

官方共分了11个Patch来提交对于Join优化器的增强，当然其中包含了对优化器和执行器分离更进一步重构，我们先来看看官方是怎么提交这样的重大重构的。

[Basic] 动态规划查询超图算法（DPhyp-Hypergraph partitioning algorithm）官方首先实现了基于DPhyp的动态规划查询超图算法，论文可以搜索《Dynamic Programming Strikes Back》。数据库中关于Join ordering算法有很多，引用2，3中的作者已经做了详尽的解释。我这里只做简单的介绍。

每一个Query，都可以定义为一个无向Query Graph，包括查询中的所有关系R1，R2，…，Rn作为节点；连接谓词表达式作为边，如a1 = a2 （a1 ∈ Ri，a2 ∈ Rj）；连接谓词中包含常量会形成自边（self-edge），如a1 = const (a1 ∈ Ri)；大部分的自边在Join算法里是不考虑的，因为它会被下推下图。例如对于 select * from Student s, Attend a, Lecture l, Professor p where s.sno = a.asno and a.alno = l.lno and l.lpno = p.pno and p.pname = ‘Larson’，有如下Query Graph结构：

对于Join Tree，一般会有以下几种：left-deep tree、right-deep tree、zigzag tree和bushy tree。前三种是属于线性Join tree。MySQL之前采取左深树，为了考虑更好的支持Hash Join和NestLoop Join的选择，现在开始考虑Bushy Tree了。为了避免任何时候的笛卡尔积Join，线性Join的Join ordering算法通常很简单。那么为什么要引入复杂的Bushy Tree。假设定义Query(R1, R2, R3)有如下属性，y |R1| = 10, |R2| = 20, |R3| = 20, |R4| = 10, f1,2 = 0.01, f2,3 = 0.5, f3,4 = 0.01。||代表行数，fn,m代表Rn和Rm的选择率，可以看到Bushy Tree有更好的执行效率。

不过遗憾的是，Bushy Tree的搜索可能性非常大：

因此，原始左深树使用的Greedy Heuristics算法，在Bushy Tree下，计算Join Ordering通常使用动态规划算法（DPccp和DPhyp）。

DPccp的算法如下：

但是DPccp有很多限制：复杂谓词，涉及到多个表（R1，R2，R3）做为连接，例如：R1.a + R2.b + R3.c = R4.d + R5.e + R6.f ；只支持inner joins；因此引入了新的基于Hypergraph的算法DPhyp。

select *
from R1 r1, R2 r2, R3 r3,
R4 r4, R5 r5, R6 r6
where r1.a=r2.a and r2.b=r3.c and
r4.d=r5.d and r5.e=r6.e and
abs(r1.f + r3.f )
= abs(r4.g + r6.g)

介绍算法先介绍下基本概念超图（hypergraph）相比普通的图，其特点是图中的节点是一个集合，称为超节点（hypernode），图中的边所连接的是超节点，即连接两个集合。这类边称为超边（hyperedge）。超图就是由超节点和超边作为最基本元素而构成的。有了超图那么上面的Join Graph可以变成：

由于使用DPccp和Top-Down Partition Search，不能够解决outer join，antijoin的不能自由重排的算法。

MySQL目前采用Bitmap（64bit）来表示，假设Join table个数不会超过61个，看下它的定义

+struct Hyperedge {
+  // The endpoints (hypernodes) of this hyperedge. See the comment about
+  // duplicated edges in Node.
+  //
+  // left and right may not overlap, and both must have at least one bit set.
+  NodeMap left;
+  NodeMap right;
+};
+
+struct Hypergraph {
+  std::vector<Node> nodes;  // Maximum 8*sizeof(NodeMap) elements.
+  std::vector<Hyperedge> edges;
+
+  void AddNode();
+  void AddEdge(NodeMap left, NodeMap right);
+};

基本算法流程如下：

找到一个图中种子节点Ri
不断增加i去找hyperedges，不考虑不连接的和已经处理过的。
对于每一个连通子图subgraph (csg)，再重复1和2步骤，找出一个仍然可以连通子图(complement, cmp)，然后连接这个图的cmp成为更大的连通子图(csg-cmp-pair).
当找到一个csg-cmp-pair，就形成一个可以进行估算的subjoin。

感兴趣可以阅读相应的论文和MySQL的代码（sql/join_optimizer）。

QEP_TAB和执行器Iterator解藕，重新来设置InnoDB row buffer

众所周知，QEB_TAB结构上承载了很多信息，除了上面表访问和Join方法的信息之外，还有InnoDB row buffer、表访问的优化访问方式（ref/range/loose scan/first match/materialize）、附加属性（having/distinct/sort/icp/lateral derived/mrr/cte）、基本物理表结构TABLE_LIST等。作为删除QEP_TAB的基础，首先先做了和执行器的解藕工作，Iterator和QEP_TAB分离。

 class TableScanIterator final : public TableRowIterator {
  public:
-  // Accepts nullptr for qep_tab; qep_tab is used only for setting up record
-  // buffers.
-  //
-  // The pushed condition can be nullptr.
+  // “expected_rows” is used for scaling the record buffer.
+  // If zero or less, no record buffer will be set up.
   //
   // "examined_rows", if not nullptr, is incremented for each successful Read().
-  TableScanIterator(THD *thd, TABLE *table, QEP_TAB *qep_tab,
+  TableScanIterator(THD *thd, TABLE *table, double expected_rows,
                     ha_rows *examined_rows);

接下来解藕

-static bool init_index_and_record_buffer(const QEP_TAB *qep_tab, handler *file,
+static bool init_index(TABLE *table, handler *file, uint idx, bool sorted) {

-bool set_record_buffer(const QEP_TAB *tab);
+bool set_record_buffer(TABLE *table, double expected_rows_to_fetch);

=>

-  return init_index_and_record_buffer(m_qep_tab, m_qep_tab->table()->file,
-                                      m_ref->key, m_use_order);
+  if (table()->file->inited) return false;
+  if (init_index(table(), table()->file, m_ref->key, m_use_order)) {
+    return true;
+  }
+  return set_record_buffer(table(), m_expected_rows);

实现CostingReceiver和转化查询块select_lex成为超图hypergraph

MySQL 8.0.23提供了支持hypergraph的优化器模型的第一个原型版本，通过set optimizer_switch=”hypergraph_optimizer=on”;来打开，主要和原有的优化器区别在于：

不再局限于左深树的执行计划
用DPhyp动态规划算法代替了强力算和启发式的剪枝方式，减少了搜索空间，当然还有一些限制
Hash join成为主要的选择方式
直接和AccessPath互通，而非直接生成Iterators

主要通过FindBestQueryPlan函数来实现，逻辑如下：

先判断是否属于新优化器可以支持的Query语法（CheckSupportedQuery），不支持的直接返回错误ER_HYPERGRAPH_NOT_SUPPORTED_YET
转化top_join_list变成JoinHypergraph结构。由于Hypergraph是比较独立的算法层面的实现，JoinHypergraph结构用来更好的把数据库的结构包装到Hypergraph的edges和nodes的概念上的。
通过EnumerateAllConnectedPartitions实现论文中的DPhyp算法
CostingReceiver类包含了过去JOIN planning的主要逻辑，包括根据cost选择相应的访问路径，根据DPhyp生成的子计划进行评估，保留cost最小的子计划。
得到root_path后，接下来处理group/agg/having/sort/limit的。对于Group by操作，目前Hypergraph使用sorting first + streaming aggregation的方式。

FindBestQueryPlan最终返回确定的执行计划root_path后，通过CreateIteratorFromAccessPath函数生成对应的执行Iterator树，在Iterator执行器中执行。

举例说明：

两个连通子图

root:test> explain format=tree select * from t1,t2,t3,t4 where t2.f2 = t1.a and t1.a = t3.a;
+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| EXPLAIN                                                                                                                                                                                                                                                                                                                                                                                                                                                          |
+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| -> Hash cartesian product (no condition)  (cost=1.83 rows=2)
    -> Inner hash join (t2.f2 = t1.a)  (cost=1.55 rows=2)
        -> Table scan on t2  (cost=0.25 rows=2)
        -> Hash
            -> Inner hash join (t1.a = t3.a)  (cost=1.27 rows=1)
                -> Table scan on t1  (cost=1.00 rows=1)
                -> Hash
                    -> Table scan on t3  (cost=0.25 rows=1)
    -> Hash
        -> Table scan on t4  (cost=0.25 rows=1)
 |

一个连通子图

root:test> explain format=tree select * from t1,t2,t3,t4 where t2.f2 = t1.a and t1.a = t3.a and t2.f2 = t4.pk and t1.a = t4.pk;
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| EXPLAIN                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |
+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------+
| -> Inner hash join (t2.f2 = t4.pk), (t1.a = t4.pk)  (cost=1.83 rows=2)
    -> Inner hash join (t2.f2 = t1.a)  (cost=1.55 rows=2)
        -> Table scan on t2  (cost=0.25 rows=2)
        -> Hash
            -> Inner hash join (t1.a = t3.a)  (cost=1.27 rows=1)
                -> Table scan on t1  (cost=1.00 rows=1)
                -> Hash
                    -> Table scan on t3  (cost=0.25 rows=1)
    -> Hash
        -> Table scan on t4  (cost=0.25 rows=1)
 |

通过打开opt_trace来看下整个过程

{
  "steps": [
    {
      "join_preparation": {
        "select#": 1,
        "steps": [
          {
            "expanded_query": "/* select#1 */ select `t1`.`a` AS `a`,`t2`.`f2` AS `f2`,`t3`.`a` AS `a`,`t3`.`b` AS `b`,`t4`.`pk` AS `pk`,`t4`.`col_int_nokey` AS `col_int_nokey`,`t4`.`col_int_key` AS `col_int_key`,`t4`.`col_varchar_nokey` AS `col_varchar_nokey` from `t1` join `t2` join `t3` join `t4` where ((`t2`.`f2` = `t1`.`a`) and (`t2`.`f2` = `t4`.`col_int_key`))"
          }
        ]
      }
    },
    {
      "join_optimization": {
        "select#": 1,
        "steps": [
          {
            "condition_processing": {
              "condition": "WHERE",
              "original_condition": "((`t2`.`f2` = `t1`.`a`) and (`t2`.`f2` = `t4`.`col_int_key`))",
              "steps": [
                {
                  "transformation": "equality_propagation",
                  "resulting_condition": "((`t2`.`f2` = `t1`.`a`) and (`t2`.`f2` = `t4`.`col_int_key`))"
                },
                {
                  "transformation": "trivial_condition_removal",
                  "resulting_condition": "((`t2`.`f2` = `t1`.`a`) and (`t2`.`f2` = `t4`.`col_int_key`))"
                }
              ]
            }
          },
          {
            "substitute_generated_columns": {
            }
          },
          {
            "join_optimizer": [
              "Join list after simplification:",
              "* t4  join_type=inner",
              "* t3  join_type=inner",
              "* t2  join_type=inner",
              "* t1  join_type=inner",
              "",
              "Made this relational tree; WHERE condition is ((t2.f2 = t1.a) and (t2.f2 = t4.col_int_key)):",
              "* Inner join (no join conditions)",
              "  * Inner join (no join conditions)",
              "    * Inner join (no join conditions)",
              "      * t1",
              "      * t2",
              "    * t3",
              "  * t4",
              "",
              "After pushdown; remaining WHERE conditions are (none):",
              "* Inner join (equijoin condition = (t2.f2 = t4.col_int_key))",
              "  * Cartesian product",
              "    * Inner join (equijoin condition = (t2.f2 = t1.a))",
              "      * t1",
              "      * t2",
              "    * t3",
              "  * t4",
              "",
              "Selectivity of join (t2.f2 = t1.a):",
              " - found an index in t1.a for (t2.f2 = t1.a), selectivity = 1.000",
              "Selectivity of join [cartesian product]:",
              "Selectivity of join (t2.f2 = t4.col_int_key):",
              " - found an index in t4.col_int_key for (t2.f2 = t4.col_int_key), selectivity = 1.000",
              "",
              "Constructed hypergraph:",
              "digraph G {  # 3 edges",
              "  t1 -> t2 [label=\"(t2.f2 = t1.a)\"]",
              "  e2 [shape=circle,width=.001,height=.001,label=\"\"]",
              "  t1 -> e2 [arrowhead=none,label=\"\"]",
              "  t2 -> e2 [arrowhead=none,label=\"\"]",
              "  e2 -> t3 [label=\"[cartesian product]\"]",
              "  t2 -> t4 [label=\"(t2.f2 = t4.col_int_key)\"]",
              "}",
              "",
              "Enumerating subplans:",
              "Found node t4 [rows=1, cost=0.2]",
              "Found node t3 [rows=1, cost=0.2]",
              "Found node t2 [rows=2, cost=0.2]",
              "Found sets {t2} and {t4}, connected by condition (t2.f2 = t4.col_int_key) [rows=2, cost=0.5]",
              " - first alternative for this join, keeping",
              "Found node t1 [rows=1, cost=1.0]",
              "Found sets {t2} and {t1}, connected by condition (t2.f2 = t1.a) [rows=2, cost=1.3]",
              " - first alternative for this join, keeping",
              "Found sets {t2,t4} and {t1}, connected by condition (t2.f2 = t1.a) [rows=2, cost=1.6]",
              " - first alternative for this join, keeping",
              "Found sets {t1,t2} and {t4}, connected by condition (t2.f2 = t4.col_int_key) [rows=2, cost=1.6]",
              " - more expensive than old cost 1.6, discarding",
              "Found sets {t1,t2} and {t3}, connected by condition [cartesian product] [rows=2, cost=1.6]",
              " - first alternative for this join, keeping",
              "Found sets {t1,t2,t3} and {t4}, connected by condition (t2.f2 = t4.col_int_key) [rows=2, cost=1.8]",
              " - first alternative for this join, keeping",
              "Found sets {t1,t2,t4} and {t3}, connected by condition [cartesian product] [rows=2, cost=1.8]",
              " - more expensive than old cost 1.8, discarding",
              "",
              "Enumerated 9 subplans."
            ]
          }
        ]
      }
    }
  ]
}

可以看到官方MySQL还提供了查看Graph图的Json格式可视化脚本，我们可以通过online graph看到连通图：

数据库内核月报－ 2021 / 02

MySQL · 源码解析 · MySQL 8.0.23 Hypergraph Join Optimizer代码详解

MySQL JOIN简介

Hypergraph Join Optimizer

基本算法流程如下：

QEP_TAB和执行器Iterator解藕，重新来设置InnoDB row buffer

实现CostingReceiver和转化查询块select_lex成为超图hypergraph

参考资料：