关于PostgreSQL中的组合索引之一(b-tree篇)

1. 问题

有时候查询中会带有多个字段的查询条件，但是其中任何单个字段的选择率都不高，但是多个字段组合起来却有比较好的选择率。这种场景是bitmap索引大显身手的地方，但是bitmap索引对更新性能的影响相当大，不适合OLTP场景。PG不支持bitmap索引，但是有一个临时的内存中的类似bitmap索引的东西，叫“Bitmap Index Scan”。
除了Bitmap Index Scan，多字段索引也是一种选择，但是两种方法的性能有没有差异呢？下面作个测试看看。

2. 测试环境

测试环境在一个PC的虚拟机上
宿主机
  CPU:AMD Athlon II X4 640 3.0GHz
  MEM:6G
  OS:Win7 64bit
  虚拟机所在存储:Apacer A S510S 128GB
虚拟机
  CPU：4 core
  MEM: 2G
  OS:CentOS release 6.5 (Final)
  PostgreSQL:9.3.4(shared_buffers = 128MB,其它都是默认值)

3. 测试数据

postgres=# create table tb1(c1 int,c2 int);
CREATE TABLE
postgres=# insert into tb1 select round(random()*100),round(random()*1000) from generate_series(1,10000000);
INSERT 0 10000000
postgres=# select pg_size_pretty(pg_table_size('tb1'));
 pg_size_pretty
----------------
 346 MB
(1 row)

4. 性能对比测试

4.1 全表扫描

postgres=# \timing
Timing is on.
postgres=# select count(*) from tb1 where c1=99 and c2=999;
 count
-------
    92
(1 row)

Time: 1376.393 ms

4.2 c1单索引扫描

postgres=# create index tb1_idx1 on tb1(c1);
CREATE INDEX
Time: 65308.131 ms
postgres=# select pg_size_pretty(pg_relation_size('tb1_idx1'));
 pg_size_pretty
----------------
 214 MB
(1 row)

Time: 2.659 ms
postgres=# explain (analyze,buffers) select count(*) from tb1 where c1=99 and c2=999;
                                                             QUERY PLAN
-------------------------------------------------------------------------------------------------------------------------------------
 Aggregate (cost=47675.20..47675.21 rows=1 width=0) (actual time=1267.921..1267.921 rows=1 loops=1)
   Buffers: shared read=39978
   -> Bitmap Heap Scan on tb1 (cost=1891.96..47674.95 rows=99 width=0) (actual time=40.726..1267.631 rows=92 loops=1)
         Recheck Cond: (c1 = 99)
         Rows Removed by Index Recheck: 7363157
         Filter: (c2 = 999)
         Rows Removed by Filter: 99794
         Buffers: shared read=39978
         -> Bitmap Index Scan on tb1_idx1 (cost=0.00..1891.93 rows=102333 width=0) (actual time=30.829..30.829 rows=99886 loops=1)
               Index Cond: (c1 = 99)
               Buffers: shared read=276
 Total runtime: 1267.961 ms
(12 rows)

Time: 1268.916 ms

c1单索引的选择率只有1/100，对查询性能提升毫无作用。

4.3 c2单索引扫描

postgres=# drop index tb1_idx1 ;
DROP INDEX
Time: 41.062 ms
postgres=# create index tb1_idx2 on tb1(c2);
CREATE INDEX
Time: 50313.915 ms
postgres=# select pg_size_pretty(pg_relation_size('tb1_idx2'));
 pg_size_pretty
----------------
 214 MB
(1 row)

Time: 0.915 ms
postgres=# explain (analyze,buffers) select count(*) from tb1 where c1=99 and c2=999;
                                                          QUERY PLAN
-------------------------------------------------------------------------------------------------------------------------------
 Aggregate (cost=23558.69..23558.70 rows=1 width=0) (actual time=74.215..74.215 rows=1 loops=1)
   Buffers: shared hit=1948 read=6954
   -> Bitmap Heap Scan on tb1 (cost=180.85..23558.45 rows=99 width=0) (actual time=5.462..73.883 rows=92 loops=1)
         Recheck Cond: (c2 = 999)
         Filter: (c1 = 99)
         Rows Removed by Filter: 9800
         Buffers: shared hit=1948 read=6954
         -> Bitmap Index Scan on tb1_idx2 (cost=0.00..180.82 rows=9652 width=0) (actual time=2.414..2.414 rows=9892 loops=1)
               Index Cond: (c2 = 999)
               Buffers: shared read=30
 Total runtime: 74.298 ms
(11 rows)

Time: 76.732 ms

c1单索引的选择率有1/1000，性能提升很明显。

4.4 c1+c2索引bitmap扫描

postgres=# create index tb1_idx1 on tb1(c1);
CREATE INDEX
Time: 56792.281 ms
postgres=# explain (analyze,buffers) select count(*) from tb1 where c1=99 and c2=999;
                                                                QUERY PLAN

-------------------------------------------------------------------------------------------------------------------------------------
------
 Aggregate (cost=2456.74..2456.75 rows=1 width=0) (actual time=50.347..50.348 rows=1 loops=1)
   Buffers: shared hit=6587 read=343
   -> Bitmap Heap Scan on tb1 (cost=2073.06..2456.49 rows=99 width=0) (actual time=39.969..50.312 rows=92 loops=1)
         Recheck Cond: ((c2 = 999) AND (c1 = 99))
         Rows Removed by Index Recheck: 7291
         Buffers: shared hit=6587 read=343
         -> BitmapAnd (cost=2073.06..2073.06 rows=99 width=0) (actual time=37.864..37.864 rows=0 loops=1)
               Buffers: shared hit=30 read=276
               -> Bitmap Index Scan on tb1_idx2 (cost=0.00..180.82 rows=9652 width=0) (actual time=3.091..3.091 rows=9892 loops=1)
                     Index Cond: (c2 = 999)
                     Buffers: shared hit=30
               -> Bitmap Index Scan on tb1_idx1 (cost=0.00..1891.93 rows=102333 width=0) (actual time=33.030..33.030 rows=99886 loo
ps=1)
                     Index Cond: (c1 = 99)
                     Buffers: shared read=276
 Total runtime: 50.484 ms
(15 rows)

Time: 52.287 ms

c1+c2索引bitmap扫描性能进一步提升。（这个性能提升也可能仅仅是因为buffers的hit命中率提升）

4.5 多字段索引扫描

postgres=# create index tb1_idx3 on tb1(c1,c2);
CREATE INDEX
Time: 67824.333 ms
postgres=# select pg_size_pretty(pg_relation_size('tb1_idx3'));
 pg_size_pretty
----------------
 214 MB
(1 row)

Time: 0.835 ms
postgres=# explain (analyze,buffers) select count(*) from tb1 where c1=99 and c2=999;
                                                       QUERY PLAN
-------------------------------------------------------------------------------------------------------------------------
 Aggregate (cost=389.13..389.14 rows=1 width=0) (actual time=0.580..0.580 rows=1 loops=1)
   Buffers: shared hit=92 read=3
   -> Bitmap Heap Scan on tb1 (cost=5.45..388.89 rows=99 width=0) (actual time=0.298..0.566 rows=92 loops=1)
         Recheck Cond: ((c1 = 99) AND (c2 = 999))
         Buffers: shared hit=92 read=3
         -> Bitmap Index Scan on tb1_idx3 (cost=0.00..5.42 rows=99 width=0) (actual time=0.279..0.279 rows=92 loops=1)
               Index Cond: ((c1 = 99) AND (c2 = 999))
               Buffers: shared read=3
 Total runtime: 0.651 ms
(9 rows)

Time: 3.912 ms

由此可见，本例中，多字段索引的效率相当高。

5. 其它

5.1 多字段索引的适用条件

------------------------------------------------------------------
一个多字段的 B-tree 索引可以用在包含索引字段子集的查询条件里，不过， 如果在前导字段(最左边)上有约束条件，那么效率最高。准确的规则是前导字段上的等于约束， 加上第一个没有等于约束的非等于约束字段，将用于限制所扫描的索引范围。 将检查这两个字段右边字段上的索引以减少对表的访问，但是并不减少需要扫描的索引。比如， 假如我们有一个在(a, b, c)上的索引，查询条件是WHERE a = 5 AND b >= 42 AND c < 77， 那么索引就需要先扫描所有a= 5 且b= 42 ，直到所有a = 5 的记录扫描完毕。那些c >= 77的索引条目将被忽略，但是他们仍然会被扫描。 这个索引原则上仍然会被用于那些在b和/或c上有约束， 但是在a上没有约束的查询，但是就必须扫描整个索引了。因此，在大多数这种情况下， 优化器会选择顺序扫描表，而不使用索引。
------------------------------------------------------------------

5.2 多字段索引的原理

b-tree多字段索引的原理很简单，就是把多个字段，按定义索引时的先后顺序排序，所以越靠前的字段越重要。
下面是b-tree多字段索引条目内容的一个例子。

postgres=# \d tb1
      Table "public.tb1"
 Column | Type | Modifiers
--------+---------+-----------
 id | integer |
 name | text |
Indexes:
    "tb1_idx2" btree (id, name)

postgres=# insert into tb1 values(1,'aaaa');
INSERT 0 1
postgres=# create extension pageinspect;
CREATE EXTENSION
postgres=# SELECT * FROM bt_page_items('tb1_idx2', 1);
 itemoffset | ctid | itemlen | nulls | vars | data
------------+-------+---------+-------+------+-------------------------------------------------
          1 | (0,5) | 24 | f | t | 01 00 00 00 0b 61 61 61 61 00 00 00 00 00 00 00
(1 row)

postgres=# select 'a'::bytea;
 bytea
-------
 \x61
(1 row)