[DRILL-5254] Enhance default reduction factors in optimizer - ASF JIRA

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Details

Type: Improvement
Status: Resolved
Priority: Major
Resolution: Won't Fix
Affects Version/s: 1.9.0
Fix Version/s: Future
Component/s: None
Labels:
- performance
- tuning

Description

Drill uses Calcite for query parsing and optimization. Drill uses Calcite's default selectivity (reduction factor) rules to compute the number of rows removed by a filter.

The default rules appear to be overly aggressive in estimating reductions. In a production use case, an input with 4 billion rows was estimated to return just 40K rows from a filter. That is, the filter estimated a 1/1,000,000 reduction in rows. As it turns out, the actual reduction was closer to 1/2.

The result was that the planner compared the expected 40K rows against another input of 2.5 million rows, and decided the 40K rows would be best on the build side of a hash join. When confronted with the actual 3 billion rows, the hash join ran out of memory.

The moral of the story is that, in Drill, it is worth being conservative when planning for memory-intensive operations.

The (sanitized) filter is the following, annotated with (a guess at) the default reduction factors in each term:

col1_s20 in ('Value1','Value2','Value3','Value4',
                     'Value5','Value6','Value7','Value8','Value9') -- 25%
AND col2_i <=3 -- 25%
AND col3_s1 = 'Y' -- 15%
AND col4_s1 = 'Y' -- 15%
AND col5_s6 not like '%str1%' -- 25%
AND col5_s6 not like '%str2%' -- 25%
AND col5_s6 not like '%str3%' -- 25%
AND col5_s6 not like '%str4%' -- 25%

Total reduction is something like:

.25 * .25 * .15 ^ 2 * .25 ^ 4 = 0.000005

Filter estimation is a known hard problem. In general, one needs statistics and other data, and even then the estimates are just guesses.

Still it is possible to ensure that the defaults are at least unbiased. That is if we assume that the probability of A LIKE B being 25%, then the probability of A NOT LIKE B should be 75%, not also 25%.

This JIRA suggests creating an experimental set of defaults based on the "core" Calcite defaults, but with other reduction factors derived using the laws of probability. In particular:

Operator	Revised	Explanation	Calcite Default
=	0.15	Default in Calcite	0.15
<>	0.85	1 - p(=)	0.5
<	0.425	p(<>) / 2	0.5
>	0.425	p(<>) / 2	0.5
<=	0.575	p(<) + p(=)	0.5
>=	0.575	p(>) + p(=)	0.5
LIKE	0.25	Default in Calcite	0.25
NOT LIKE	0.75	1 - p(LIKE)	0.25
NOT NULL	0.90	Default in Calcite	0.90
IS NULL	0.10	1 - p(NOT NULL)	0.25
val IS TRUE	0.5	1 / 2	0.25
val IS FALSE	0.5	1 / 2	0.25
val IS NOT TRUE	0.55	(1 + p(NULL)) / 2	0.25
val IS NOT FALSE	0.55	(1 + p(NULL)) / 2	0.25
expr IS TRUE	Varies	p(expr)	0.25
expr IS FALSE	Varies	1 - p(expr)	0.25
expr IS NOT TRUE	Varies	p(expr IS FALSE)	0.25
expr IS NOT FALSE	Varies	p(expr IS TRUE)	0.25
A OR B	Varies	min(p(A) + p(B), 0.5)	0.5
A AND B	Varies	p(A ^ B) = p(A) * p(B)	Same
IN (a)	0.15	p(=)	0.25
x IN (a, b, c, ...)	Varies	p(x = a v x = b v x = c v ...)	0.25
NOT A	Varies	1 - p(A)	0.25
BETWEEN a AND b	0.33	p(<= ^ >=)	0.25
NOT BETWEEN a AND b	0.67	1 - p(BETWEEN)	0.25

The Calcite defaults were identified by inspection and verified by tests. The Calcite rules make sense if one considers conditional probability: that the user applied a particular expression to the data with the expectation that given that data set, the expression matches 25% of the rows.

The probability of the IS NOT TRUE statement assumes the presence of nulls, while IS TRUE does not. This is an example of conditional probability. If the user asks if something is TRUE, we can assume that they are nor worried about nulls. If they ask if it is NOT FALSE, the only justification for such syntax is to include nulls. Since we assume nulls (when present) make up 10% of data, in such a case, half the non-null data is true, half is false.

Note that, in the proposed implementation, each expression in an IS TRUE or similar clause is considered as a constant. That is, the following deliver different reduction factors:

a = 10
(a = 10) IS TRUE

One could argue that the second should give the selectivity for "a = 10", but the code (at present) treats this the same as "b IS TRUE" where b just happens to be "a = 10".

The rule for OR caps the reduction factor at 0.5 per standard practice. We assume values are independent, so the reduction is simply the sum of the individual items. (If data consists of "a", "b", "c" and "d", then p("a") = 25% and p("a" | "b" | "c" | "d" ) = 100%.

The rule for BETWEEN arises because Calcite (or Drill?) rewrites a BETWEEN b AND c as a >= b AND a <= c.

With the revised rules, the example WHERE reduction becomes:

col1_s20 in ('Value1','Value2','Value3','Value4',
                     'Value5','Value6','Value7','Value8','Value9') -- 50%
AND col2_i <=3 -- 57%
AND col3_s1 = 'Y' -- 15%
AND col4_s1 = 'Y' -- 15%
AND col5_s6 not like '%str1%' -- 85%
AND col5_s6 not like '%str2%' -- 85%
AND col5_s6 not like '%str3%' -- 85%
AND col5_s6 not like '%str4%' -- 85%

.5 * .57 * .15^2 * .85^4 = 0.003

The new rules are not a panacea: they are still just guesses. However, they are unbiased guesses based on the rules of probability which result in more conservative reductions of filters. The result may be better plans in queries with large conjunctions (large number of expressions AND'ed together.)