This document summarizes optimization techniques for queries involving grouping and aggregation in PostgreSQL. It discusses avoiding sorts through hash aggregation, count distinct optimization, handling ordered aggregates, summation optimization for data types and zero values, and denormalized data aggregation. Specific techniques covered include increasing work_mem, two-level hash aggregation, extensions for count distinct and hyperloglog, sorting arrays separately, and using MIN to correlate denormalized data in grouping.

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PostgreSQL
Performance for queries with grouping
Alexey Bashtanov, Brandwatch, Brighton
05 Jul 2016

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What is it all about?
This talk will cover optimisation of
Grouping
Aggregation
Unfortunately it will not cover optimisation of
Getting the data
Filtering
Joins
Window functions
Other data transformations

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Outline
1 What is a grouping?
2 How does it work?
Aggregation functions under the hood
Grouping algorithms
3 Optimisation: avoid sorts
Simple group-by
Count distinct values
Ordered aggregates
4 Summation optimisation
5 Denormalized data aggregation
6 Arg-maximum
7 Some magic: loose index scan
8 The future: parallel execution

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What is a grouping?

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What is a grouping?
What do we call a grouping/aggregation operation?
An operation of splitting input data into several classes and
then compilation each class into one row.
3
32 21 1
3
3
3
3
1
1
2
2 15
2
2
2
2
3
3
1
1 8
3
3
2
2
3
3
1
1 9

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Examples
SELECT department_id,
avg(salary)
FROM employees
GROUP BY department_id
SELECT DISTINCT department_id
FROM employees

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Examples
SELECT DISTINCT ON (department_id)
department_id,
employee_id,
salary
FROM employees
ORDER BY department_id,
salary DESC

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Examples
SELECT max(salary)
FROM employees
SELECT salary
FROM employees
ORDER BY salary DESC
LIMIT 1

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How does it work?

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Aggregation functions under the hood
INITCOND SFUNC
Input data
state SFUNC
Input data
state SFUNC
Input data
state
FINALFUNC
Result
An aggregate function is defined by:
State, input and output types
Initial state (INITCOND)
Transition function (SFUNC)
Final function (FINALFUNC)

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Aggregation functions under the hood
state = 0 state += input
2
2 state += input
3
5 state += input
7
12
=
sum=12
SELECT sum(column1),
avg(column1)
FROM (VALUES (2), (3), (7)) _

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Aggregation functions under the hood
cnt = 0
sum = 0
cnt++
sum+=input
2
cnt=1
sum=2
cnt++
sum+=input
3
cnt=2
sum=5
cnt++
sum+=input
7
cnt=3
sum=12
sum / cnt
avg=4
SELECT sum(column1),
avg(column1)
FROM (VALUES (2), (3), (7)) _

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Aggregation functions under the hood
SFUNC and FINALFUNC functions can be written in
C — fast (SFUNC may reuse state variable)
SQL
PL/pgSQL — SLOW!
any other language
SFUNC and FINALFUNC functions can be declared STRICT
(i.e. not called on null input)

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Grouping algorithms
PostgreSQL uses 2 algorithms to feed aggregate functions by
grouped data:
GroupAggregate: get the data sorted and apply
aggregation function to groups one by one
HashAggregate: store state for each key in a hash table

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GroupAgg
1 3 1 2 2 3 1 3 2 1 state: 0

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GroupAgg
1 3 1 2 2 3 1 3 2 1 state: 0
1 3 1 2 2 3 1 3 state: 3

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GroupAgg
1 3 1 2 2 3 1 3 2 1 state: 0
1 3 1 2 2 3 1 3 state: 3
1 3 1 2 2 state: 4 6

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GroupAgg
1 3 1 2 2 3 1 3 2 1 state: 0
1 3 1 2 2 3 1 3 state: 3
1 3 1 2 2 state: 4 6
1 3 1 state: 0 8 6

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GroupAgg
1 3 1 2 2 3 1 3 2 1 state: 0
1 3 1 2 2 3 1 3 state: 3
1 3 1 2 2 state: 4 6
1 3 1 state: 0 8 6
5 8 6

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HashAggregate
1 2 3 2 3 1 2 1 3 1 state: 0

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HashAggregate
1 2 3 2 3 1 2 1 3 1 state: 0
1 2 3 2 3 1 2 1 3 state: 1

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HashAggregate
1 2 3 2 3 1 2 1 3 1 state: 0
1 2 3 2 3 1 2 1 3 state: 1
1 2 3 2 3 1 2 1
state: 1
state: 3

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HashAggregate
1 2 3 2 3 1 2 1 3 1 state: 0
1 2 3 2 3 1 2 1 3 state: 1
1 2 3 2 3 1 2 1
state: 1
state: 3
1 2 3
state: 6
state: 6
state: 1

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HashAggregate
1 2 3 2 3 1 2 1 3 1 state: 0
1 2 3 2 3 1 2 1 3 state: 1
1 2 3 2 3 1 2 1
state: 1
state: 3
1 2 3
state: 6
state: 6
state: 1
state: 6
state: 8
state: 5

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HashAggregate
1 2 3 2 3 1 2 1 3 1 state: 0
1 2 3 2 3 1 2 1 3 state: 1
1 2 3 2 3 1 2 1
state: 1
state: 3
1 2 3
state: 6
state: 6
state: 1
state: 6
state: 8
state: 5
68 5

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GroupAggregate vs. HashAggregate
GroupAggregate
− Requires sorted data
+ Needs less memory
+ Returns sorted data
+ Returns data on the fly
+ Can perform
count(distinct x),
array_agg(x order by y)
etc.
+ On cardinality
misestimation will sort on
disk
HashAggregate
+ Accepts unsorted data
− Needs more memory
− Returns unsorted data
− Returns data at the end
− Can perform only basic
aggregation
− On groups count
misestimation will OOM

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Optimisation: avoid sorts

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Simple group-by: avoid sorts
Sorts are really slow. Prefer HashAggregation if possible.
100 101 102 103 104 105
106 107
0
1
2
3
4
5
6
7
Groups
Time,s
SELECT a, COUNT(*) FROM t_10m GROUP BY a
HashAgg
Sort + GroupAgg

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Simple group-by: avoid sorts
Sorts are really slow. Prefer HashAggregation if possible.
What to do if you get something like this?
EXPLAIN
SELECT region_id,
avg(age)
FROM people
GROUP BY region_id
GroupAggregate (cost=149244.84..156869.46 rows=9969 width=10)
-> Sort (cost=149244.84..151744.84 rows=1000000 width=10)
Sort Key: region_id
-> Seq Scan on people (cost=0.00..15406.00 rows=1000000 width=10)
1504.474 ms

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Simple group-by: avoid sorts
Sorts are really slow. Prefer HashAggregation if possible.
What to do if you get something like this?
EXPLAIN
SELECT region_id,
avg(age)
FROM people
GROUP BY region_id
set enable_sort to off?

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Simple group-by: avoid sorts
Sorts are really slow. Prefer HashAggregation if possible.
What to do if you get something like this?
EXPLAIN
SELECT region_id,
avg(age)
FROM people
GROUP BY region_id
set enable_sort to off? No!
GroupAggregate (cost=10000149244.84..10000156869.46 rows=9969 width=10)
-> Sort (cost=10000149244.84..10000151744.84 rows=1000000 width=10)
Sort Key: region_id
-> Seq Scan on people (cost=0.00..15406.00 rows=1000000 width=10)
1497.167 ms

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Simple group-by: avoid sorts
Sorts are really slow. Prefer HashAggregation if possible.
What to do if you get something like this?
EXPLAIN
SELECT region_id,
avg(age)
FROM people
GROUP BY region_id
Increase work_mem: set work_mem to ’100MB’
HashAggregate (cost=20406.00..20530.61 rows=9969 width=10)
-> Seq Scan on people (cost=0.00..15406.00 rows=1000000 width=10)
685.689 ms

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Simple group-by: avoid sorts
Sorts are really slow. Prefer HashAggregation if possible.
What to do if you get something like this?
EXPLAIN
SELECT region_id,
avg(age)
FROM people
GROUP BY region_id
Increase work_mem: set work_mem to ’100MB’
HashAggregate (cost=20406.00..20530.61 rows=9969 width=10)
-> Seq Scan on people (cost=0.00..15406.00 rows=1000000 width=10)
685.689 ms
Increase sanely to avoid OOM

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Simple group-by: avoid sorts
How to spend less memory to allow HashAggregation?
Don’t aggregate joined
SELECT p.region_id,
d.region_description,
avg(age)
FROM people p
JOIN regions r using (region_id)
GROUP BY region_id,
region_description
Join aggregated instead
SELECT a.region_id,
r.region_description,
a.avg_age
FROM (
SELECT region_id,
avg(age) avg_age
FROM people p
GROUP BY region_id
) a
JOIN regions r using (region_id)

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Count distinct: avoid sorts as well
How to avoid sorts for count(DISTINCT ...)?
SELECT location_id,
count(DISTINCT visitor_id)
FROM visits
GROUP BY location_id
GroupAggregate (actual time=2371.992..4832.437 rows=1000 loops=1)
Group Key: location_id
-> Sort (actual time=2369.322..3488.261 rows=10000000 loops=1)
Sort Key: location_id
Sort Method: quicksort Memory: 818276kB
-> Seq Scan on visitors (actual time=0.007..943.090 rows=10000000 loops=1)

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Count distinct: avoid sorts as well!
Two levels of HashAggregate could be faster!
SELECT location_id,
count(*)
FROM (
SELECT DISTINCT location_id,
visitor_id
FROM visits
) _
GROUP BY location_id
HashAggregate (actual time=2409.378..2409.471 rows=1000 loops=1)
Group Key: visits.location_id
-> HashAggregate (actual time=2235.069..2235.156 rows=1000 loops=1)
Group Key: visits.location_id, visits.visitor_id
-> Seq Scan on visits (actual time=0.005..884.194 rows=10000000 loops=1)

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Count distinct: avoid sorts as well!
Or use an extension by Tomáš Vondra:
https://github.com/tvondra/count_distinct
SELECT location_id,
count_distinct(visitor_id)
FROM visits
GROUP BY location_id
HashAggregate (actual time=3041.093..3041.466 rows=1000 loops=1)
Group Key: visitor_id
-> Seq Scan on visits (actual time=0.004..546.042 rows=10000000 loops=1)
Warning: this algorithm uses much memory in certain
circumstances

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Count distinct: avoid sorts as well!
There is another extension that allows to calculate approximate
number of distinct values using constant amount of memory:
https:
//github.com/aggregateknowledge/postgresql-hll
SELECT location_id,
hll_cardinality(
hll_add_agg(hll_hash_integer(c))
)
FROM visits
GROUP BY location_id
HashAggregate (actual time=3848.346..3867.570 rows=1000 loops=1)
Group Key: visitor_id
-> Seq Scan on visits (actual time=0.004..546.042 rows=10000000 loops=1)

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Count distinct: avoid sorts as well!
100 101 102 103 104
0
1
2
3
4
5
6
7
8
Distinct values per group
Time,s
Count-distinct from a 10M-rows table by 1000 groups
Sort+GroupAgg
HashAgg+HashAgg
Count_distinct ext.
Postgres_hll ext.

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Ordered aggregates: avoid massive sorts
How to avoid sorts for array_agg(...ORDER BY ...)?
SELECT
visit_date,
array_agg(visitor_id ORDER BY visitor_id)
FROM visits
GROUP BY visit_date
GroupAggregate (actual time=5433.658..8010.309 rows=10000 loops=1)
-> Sort (actual time=5433.416..6769.872 rows=4999067 loops=1)
Sort Key: visit_date
Sort Method: external merge Disk: 107504kB
-> Seq Scan on visits (actual time=0.046..581.672 rows=4999067 loops=1)

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Avoiding sorts
Might be better to sort each line separately
SELECT
visit_date,
(
select array_agg(i ORDER BY i)
from unnest(visitors_u) i
)
FROM (
SELECT visit_date,
array_agg(visitor_id) visitors_u
FROM visits
GROUP BY visit_date
) _
Subquery Scan on _ (actual time=2504.915..3767.300 rows=10000 loops=1)
-> HashAggregate (actual time=2504.757..2555.038 rows=10000 loops=1)
-> Seq Scan on visits (actual time=0.056..397.859 rows=4999067 loops=1)
SubPlan 1
-> Aggregate (actual time=0.120..0.121 rows=1 loops=10000)
-> Function Scan on unnest i (actual time=0.033..0.055 rows=500 loops=10000)

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Summation optimisation

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Summation: integer data types
smallint int bigint numeric
0
10
20
11 11
23
20
12 12 12
21
Time,s
Summating 100M numbers
9.4
9.5
sum(bigint) returns numeric was slow in 9.4 as it used
to convert every input value to numeric.

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Summation: zeroes
0 % 20 % 40 % 60 % 80 % 100 %
0
1
2
Non-zero values
Time,s
Summation of 10M numerics
SELECT SUM(a) FROM t
SELECT SUM(a) FROM t WHERE a <> 0
SELECT SUM(a) FROM t, nulls stored instead of zeroes

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Denormalized data aggregation

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Denormalized data aggregation
Sometimes we need to aggregate denormalized data
Most common solution is
SELECT account_id,
account_name,
sum(payment_amount)
FROM payments
GROUP BY account_id,
account_name
Planner does not know that account_id and account_name
correlate. It can lead to wrong estimates and suboptimal plan.

47. 31/50
Denormalized data aggregation
A bit less-known approach is
SELECT account_id,
min(account_name),
sum(payment_amount)
FROM payments
GROUP BY account_id
Works only if the type of "denormalized payload" supports
comparison operator.

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Denormalized data aggregation
Also we can write a custom aggregate function
CREATE FUNCTION frst (text, text)
RETURNS text IMMUTABLE LANGUAGE sql AS
$$ select $1; $$;
CREATE AGGREGATE a (text) (
SFUNC=frst,
STYPE=text
);
SELECT account_id,
a(account_name),
sum(payment_amount)
FROM payments
GROUP BY account_id

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Denormalized data aggregation
Or even write it in C:
https://github.com/bashtanov/argm
SELECT account_id,
anyold(account_name),
sum(payment_amount)
FROM payments
GROUP BY account_id

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Denormalized data aggregation
And what is the fastest?
It depends on the width of "denormalized payload":
1 10 100 1000 10000
dumb 366ms 374ms 459ms 1238ms 53236ms
min 375ms 377ms 409ms 716ms 16747ms
SQL 1970ms 1975ms 2031ms 2446ms 2036ms
C 385ms 385ms 408ms 659ms 436ms

51. 34/50
Denormalized data aggregation
And what is the fastest?
It depends on the width of "denormalized payload":
1 10 100 1000 10000
dumb 366ms 374ms 459ms 1238ms 53236ms
min 375ms 377ms 409ms 716ms 16747ms
SQL 1970ms 1975ms 2031ms 2446ms 2036ms*
C 385ms 385ms 408ms 659ms 436ms*
* — The more data the faster we proceed?
It is because we do not need to extract TOASTed values.

52. 35/50
Arg-maximum

53. 36/50
Arg-maximum
Max
Population of the largest
city in each country
Date of last tweet by each
author
The highest salary in each
department

54. 36/50
Arg-maximum
Max
Population of the largest
city in each country
Date of last tweet by each
author
The highest salary in each
department
Arg-max
What is the largest city in
each country
What is the last tweet by
each author
Who gets the highest
salary in each department

55. 37/50
Arg-maximum
Max is built-in. How to perform Arg-max?
Self-joins?
Window-functions?

56. 37/50
Arg-maximum
Max is built-in. How to perform Arg-max?
Self-joins?
Window-functions?
Use DISTINCT ON() (PG-specific, not in SQL standard)
SELECT DISTINCT ON (author_id)
author_id,
twit_id
FROM twits
ORDER BY author_id,
twit_date DESC

57. 37/50
Arg-maximum
Max is built-in. How to perform Arg-max?
Self-joins?
Window-functions?
Use DISTINCT ON() (PG-specific, not in SQL standard)
SELECT DISTINCT ON (author_id)
author_id,
twit_id
FROM twits
ORDER BY author_id,
twit_date DESC
But it still can be performed only by sorting, not by hashing :(

58. 38/50
Arg-maximum
We can emulate Arg-max by ordinary max and dirty hacks
SELECT author_id,
(max(array[
twit_date,
date’epoch’ + twit_id
]))[2] - date’epoch’
FROM twits
GROUP BY author_id;
But such types tweaking is not always possible.

59. 39/50
Arg-maximum
It’s time to write more custom aggregate functions
CREATE TYPE amax_ty AS (key_date date, payload int);
CREATE FUNCTION amax_t (p_state amax_ty, p_key_date date, p_payload int)
RETURNS amax_ty IMMUTABLE LANGUAGE sql AS
$$
SELECT CASE WHEN p_state.key_date < p_key_date
OR (p_key_date IS NOT NULL AND p_state.key_date IS NULL)
THEN (p_key_date, p_payload)::amax_ty
ELSE p_state END
$$;
CREATE FUNCTION amax_f (p_state amax_ty) RETURNS int IMMUTABLE LANGUAGE sql AS
$$ SELECT p_state.payload $$;
CREATE AGGREGATE amax (date, int) (
SFUNC = amax_t,
STYPE = amax_ty,
FINALFUNC = amax_f,
INITCOND = ’(,)’
);
SELECT author_id,
amax(twit_date, twit_id)
FROM twits
GROUP BY author_id;

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Arg-maximum
Argmax is similar to amax, but written in C
https://github.com/bashtanov/argm
SELECT author_id,
argmax(twit_date, twit_id)
FROM twits
GROUP BY author_id;

61. 41/50
Arg-maximum
Who wins now?
1002 3332 10002 33332 50002
DISTINCT ON 6ms 42ms 342ms 10555ms 30421ms
Max(array) 5ms 47ms 399ms 4464ms 10025ms
SQL amax 38ms 393ms 3541ms 39539ms 90164ms
C argmax 5ms 37ms 288ms 3183ms 7176ms

62. 41/50
Arg-maximum
Who wins now?
1002 3332 10002 33332 50002
DISTINCT ON 6ms 42ms 342ms 10555ms 30421ms
Max(array) 5ms 47ms 399ms 4464ms 10025ms
SQL amax 38ms 393ms 3541ms 39539ms 90164ms
C argmax 5ms 37ms 288ms 3183ms 7176ms
SQL amax finally outperforms DISTINCT ON on 109-ish rows

63. 42/50
Some magic: loose index scan

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Loose index scan
Slow distinct, max or arg-max query?
Sometimes we can fetch the rows one-by-one using index:
3 2 1 4 2 2 1 3 31 0
CREATE TABLE balls(colour_id int, label int);
INSERT INTO balls ...
CREATE INDEX ON balls(colour_id);
-- find the very first colour
SELECT colour_id FROM balls
ORDER BY colour_id LIMIT 1;
-- find the next colour
SELECT colour_id FROM balls
WHERE colour_id > ?
ORDER BY colour_id LIMIT 1;
-- and so on ...

65. 44/50
Loose index scan
CREATE FUNCTION loosescan() RETURNS
TABLE (o_colour_id int) AS $$
BEGIN
o_colour_id := -1; --less than all real ids
LOOP
SELECT colour_id
INTO o_colour_id
FROM balls
WHERE colour_id > o_colour_id
ORDER BY colour_id LIMIT 1;
EXIT WHEN NOT FOUND; RETURN NEXT;
END LOOP;
END;
$$ LANGUAGE plpgsql;
SELECT * FROM loosescan();

66. 45/50
Loose index scan
Or better do it in pure SQL instead
WITH RECURSIVE d AS (
(
SELECT colour_id
FROM balls
ORDER BY colour_id LIMIT 1
)
UNION
SELECT (
SELECT b.colour_id
FROM balls b
WHERE b.colour_id > d.colour_id
ORDER BY b.colour_id LIMIT 1
) colour_id
FROM d
)
SELECT * FROM d WHERE colour_id IS NOT NULL;

67. 46/50
Loose index scan
One-by-one retrieval by index
+ Incredibly fast unless returns too many rows
− Needs an index
Fetching distinct values from a 10M-rows table:
101 103 105 106 107
HashAgg 1339ms 1377ms 2945ms 4086ms 5130ms
LIS proc 0ms 9ms 815ms 8004ms 80800ms
LIS SQL 0ms 6ms 555ms 5460ms 56153ms

68. 47/50
Loose index scan
It is possible to explore similar approach for max and argmax
+ Incredibly fast unless returns too many rows
− Needs an index
− SQL version needs tricks if the data types differ
1002 3332 10002 33332 50002
DISTINCT ON 6ms 42ms 342ms 10555ms 30421ms
Max(array) 5ms 47ms 399ms 4464ms 10025ms
SQL amax 38ms 393ms 3541ms 39539ms 90164ms
C argmax 5ms 37ms 288ms 3183ms 7176ms
LIS proc 2ms 6ms 12ms 42ms 63ms
LIS SQL 1ms 4ms 11ms 29ms 37ms

69. 48/50
The future: parallel execution

70. 49/50
The future: parallel execution
PostgreSQL 9.6 (currently Beta 2) introduces parallel execution
of many nodes including aggregation.
Parallel aggregation extension is already available:
http://www.cybertec.at/en/products/
agg-parallel-aggregations-postgresql/
+ Up to 30 times faster
+ Speeds up SeqScan as well
− Mostly useful for complex row operations
− Requires PG 9.5+

71. 50/50
Questions?