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8.2.1.3 Range Optimization

The range access method uses a single index to retrieve a subset of table rows that are contained within one or several index value intervals. It can be used for a single-part or multiple-part index. The following sections give a detailed description of how intervals are extracted from the WHERE clause.

8.2.1.3.1 The Range Access Method for Single-Part Indexes

For a single-part index, index value intervals can be conveniently represented by corresponding conditions in the WHERE clause, so we speak of range conditions rather than “intervals.”

The definition of a range condition for a single-part index is as follows:

  • For both BTREE and HASH indexes, comparison of a key part with a constant value is a range condition when using the =, <=>, IN(), IS NULL, or IS NOT NULL operators.

  • Additionally, for BTREE indexes, comparison of a key part with a constant value is a range condition when using the >, <, >=, <=, BETWEEN, !=, or <> operators, or LIKE comparisons if the argument to LIKE is a constant string that does not start with a wildcard character.

  • For all types of indexes, multiple range conditions combined with OR or AND form a range condition.

“Constant value” in the preceding descriptions means one of the following:

  • A constant from the query string

  • A column of a const or system table from the same join

  • The result of an uncorrelated subquery

  • Any expression composed entirely from subexpressions of the preceding types

Here are some examples of queries with range conditions in the WHERE clause: 

SELECT * FROM t1
  WHERE key_col > 1
  AND key_col < 10;

SELECT * FROM t1
  WHERE key_col = 1
  OR key_col IN (15,18,20);

SELECT * FROM t1
  WHERE key_col LIKE 'ab%'
  OR key_col BETWEEN 'bar' AND 'foo';

Some nonconstant values may be converted to constants during the constant propagation phase.

MySQL tries to extract range conditions from the WHERE clause for each of the possible indexes. During the extraction process, conditions that cannot be used for constructing the range condition are dropped, conditions that produce overlapping ranges are combined, and conditions that produce empty ranges are removed.

Consider the following statement, where key1 is an indexed column and nonkey is not indexed: 

SELECT * FROM t1 WHERE
  (key1 < 'abc' AND (key1 LIKE 'abcde%' OR key1 LIKE '%b')) OR
  (key1 < 'bar' AND nonkey = 4) OR
  (key1 < 'uux' AND key1 > 'z');

The extraction process for key key1 is as follows:

  1. Start with original WHERE clause: 

    (key1 < 'abc' AND (key1 LIKE 'abcde%' OR key1 LIKE '%b')) OR
(key1 < 'bar' AND nonkey = 4) OR
(key1 < 'uux' AND key1 > 'z')

  2. Remove nonkey = 4 and key1 LIKE '%b' because they cannot be used for a range scan. The correct way to remove them is to replace them with TRUE, so that we do not miss any matching rows when doing the range scan. Having replaced them with TRUE, we get: 

    (key1 < 'abc' AND (key1 LIKE 'abcde%' OR TRUE)) OR
(key1 < 'bar' AND TRUE) OR
(key1 < 'uux' AND key1 > 'z')

  3. Collapse conditions that are always true or false:

    • (key1 LIKE 'abcde%' OR TRUE) is always true

    • (key1 < 'uux' AND key1 > 'z') is always false

    Replacing these conditions with constants, we get: 

    (key1 < 'abc' AND TRUE) OR (key1 < 'bar' AND TRUE) OR (FALSE)

    Removing unnecessary TRUE and FALSE constants, we obtain: 

    (key1 < 'abc') OR (key1 < 'bar')

  4. Combining overlapping intervals into one yields the final condition to be used for the range scan: 

    (key1 < 'bar')

In general (and as demonstrated by the preceding example), the condition used for a range scan is less restrictive than the WHERE clause. MySQL performs an additional check to filter out rows that satisfy the range condition but not the full WHERE clause.

The range condition extraction algorithm can handle nested AND/OR constructs of arbitrary depth, and its output does not depend on the order in which conditions appear in WHERE clause.

Currently, MySQL does not support merging multiple ranges for the range access method for spatial indexes. To work around this limitation, you can use a UNION with identical SELECT statements, except that you put each spatial predicate in a different SELECT.

8.2.1.3.2 The Range Access Method for Multiple-Part Indexes

Range conditions on a multiple-part index are an extension of range conditions for a single-part index. A range condition on a multiple-part index restricts index rows to lie within one or several key tuple intervals. Key tuple intervals are defined over a set of key tuples, using ordering from the index.

For example, consider a multiple-part index defined as key1(key_part1, key_part2, key_part3), and the following set of key tuples listed in key order: 

key_part1  key_part2  key_part3
  NULL       1          'abc'
  NULL       1          'xyz'
  NULL       2          'foo'
   1         1          'abc'
   1         1          'xyz'
   1         2          'abc'
   2         1          'aaa'

The condition key_part1 = 1 defines this interval: 

(1,-inf,-inf) <= (key_part1,key_part2,key_part3) < (1,+inf,+inf)

The interval covers the 4th, 5th, and 6th tuples in the preceding data set and can be used by the range access method.

By contrast, the condition key_part3 = 'abc' does not define a single interval and cannot be used by the range access method.

The following descriptions indicate how range conditions work for multiple-part indexes in greater detail.

  • For HASH indexes, each interval containing identical values can be used. This means that the interval can be produced only for conditions in the following form: 

        key_part1 cmp const1
AND key_part2 cmp const2
AND ...
AND key_partN cmp constN;

    Here, const1, const2, … are constants, cmp is one of the =, <=>, or IS NULL comparison operators, and the conditions cover all index parts. (That is, there are N conditions, one for each part of an N-part index.) For example, the following is a range condition for a three-part HASH index: 

    key_part1 = 1 AND key_part2 IS NULL AND key_part3 = 'foo'

    For the definition of what is considered to be a constant, see Section 8.2.1.3.1, “The Range Access Method for Single-Part Indexes”.

  • For a BTREE index, an interval might be usable for conditions combined with AND, where each condition compares a key part with a constant value using =, <=>, IS NULL, >, <, >=, <=, !=, <>, BETWEEN, or LIKE 'pattern' (where 'pattern' does not start with a wildcard). An interval can be used as long as it is possible to determine a single key tuple containing all rows that match the condition (or two intervals if <> or != is used).

    The optimizer attempts to use additional key parts to determine the interval as long as the comparison operator is =, <=>, or IS NULL. If the operator is >, <, >=, <=, !=, <>, BETWEEN, or LIKE, the optimizer uses it but considers no more key parts. For the following expression, the optimizer uses = from the first comparison. It also uses >= from the second comparison but considers no further key parts and does not use the third comparison for interval construction: 

    key_part1 = 'foo' AND key_part2 >= 10 AND key_part3 > 10

    The single interval is: 

    ('foo',10,-inf) < (key_part1,key_part2,key_part3) < ('foo',+inf,+inf)

    It is possible that the created interval contains more rows than the initial condition. For example, the preceding interval includes the value ('foo', 11, 0), which does not satisfy the original condition.

  • If conditions that cover sets of rows contained within intervals are combined with OR, they form a condition that covers a set of rows contained within the union of their intervals. If the conditions are combined with AND, they form a condition that covers a set of rows contained within the intersection of their intervals. For example, for this condition on a two-part index: 

    (key_part1 = 1 AND key_part2 < 2) OR (key_part1 > 5)

    The intervals are: 

    (1,-inf) < (key_part1,key_part2) < (1,2)
(5,-inf) < (key_part1,key_part2)

    In this example, the interval on the first line uses one key part for the left bound and two key parts for the right bound. The interval on the second line uses only one key part. The key_len column in the EXPLAIN output indicates the maximum length of the key prefix used.

    In some cases, key_len may indicate that a key part was used, but that might be not what you would expect. Suppose that key_part1 and key_part2 can be NULL. Then the key_len column displays two key part lengths for the following condition: 

    key_part1 >= 1 AND key_part2 < 2

    But, in fact, the condition is converted to this: 

    key_part1 >= 1 AND key_part2 IS NOT NULL

Section 8.2.1.3.1, “The Range Access Method for Single-Part Indexes”, describes how optimizations are performed to combine or eliminate intervals for range conditions on a single-part index. Analogous steps are performed for range conditions on multiple-part indexes.

8.2.1.3.3 Equality Range Optimization of Many-Valued Comparisons

Consider these expressions, where col_name is an indexed column: 

col_name IN(val1, ..., valN)
col_name = val1 OR ... OR col_name = valN

Each expression is true if col_name is equal to any of several values. These comparisons are equality range comparisons (where the “range” is a single value). The optimizer estimates the cost of reading qualifying rows for equality range comparisons as follows:

  • If there is a unique index on col_name, the row estimate for each range is 1 because at most one row can have the given value.

  • Otherwise, the optimizer can estimate the row count for each range using dives into the index or index statistics.

With index dives, the optimizer makes a dive at each end of a range and uses the number of rows in the range as the estimate. For example, the expression col_name IN (10, 20, 30) has three equality ranges and the optimizer makes two dives per range to generate a row estimate. Each pair of dives yields an estimate of the number of rows that have the given value.

Index dives provide accurate row estimates, but as the number of comparison values in the expression increases, the optimizer takes longer to generate a row estimate. Use of index statistics is less accurate than index dives but permits faster row estimation for large value lists.

The eq_range_index_dive_limit system variable enables you to configure the number of values at which the optimizer switches from one row estimation strategy to the other. To disable use of statistics and always use index dives, set eq_range_index_dive_limit to 0. To permit use of index dives for comparisons of up to N equality ranges, set eq_range_index_dive_limit to N + 1.

eq_range_index_dive_limit is available as of MySQL 5.6.5. Before 5.6.5, the optimizer uses index dives, which is equivalent to eq_range_index_dive_limit=0.

To update table index statistics for best estimates, use ANALYZE TABLE.


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