Can spatial index help a "range - order by - limit" query
You may be able to achieve better performance by searching first in rows with higher frequencies. This can be achieved by 'granulating' the frequencies and then stepping through them procedurally, for example as follows:
--testbed and lexikon dummy data:
begin;
set role dba;
create role stack;
grant stack to dba;
create schema authorization stack;
set role stack;
--
create table lexikon( _id serial,
word text,
frequency integer,
lset integer,
width_granule integer);
--
insert into lexikon(word, frequency, lset)
select word, (1000000/row_number() over(order by random()))::integer as frequency, lset
from (select 'word'||generate_series(1,1000000) word, generate_series(1,1000000) lset) z;
--
update lexikon set width_granule=ln(frequency)::integer;
--
create index on lexikon(width_granule, lset);
create index on lexikon(lset);
-- the second index is not used with the function but is added to make the timings 'fair'
granule analysis (mostly for information and tuning):
create table granule as
select width_granule, count(*) as freq,
min(frequency) as granule_start, max(frequency) as granule_end
from lexikon group by width_granule;
--
select * from granule order by 1;
/*
width_granule | freq | granule_start | granule_end
---------------+--------+---------------+-------------
0 | 500000 | 1 | 1
1 | 300000 | 2 | 4
2 | 123077 | 5 | 12
3 | 47512 | 13 | 33
4 | 18422 | 34 | 90
5 | 6908 | 91 | 244
6 | 2580 | 245 | 665
7 | 949 | 666 | 1808
8 | 349 | 1811 | 4901
9 | 129 | 4926 | 13333
10 | 47 | 13513 | 35714
11 | 17 | 37037 | 90909
12 | 7 | 100000 | 250000
13 | 2 | 333333 | 500000
14 | 1 | 1000000 | 1000000
*/
alter table granule drop column freq;
--
function for scanning high frequencies first:
create function f(p_lset_low in integer, p_lset_high in integer, p_limit in integer)
returns setof lexikon language plpgsql set search_path to 'stack' as $$
declare
m integer;
n integer := 0;
r record;
begin
for r in (select width_granule from granule order by width_granule desc) loop
return query( select *
from lexikon
where width_granule=r.width_granule
and lset>=p_lset_low and lset<=p_lset_high );
get diagnostics m = row_count;
n = n+m;
exit when n>=p_limit;
end loop;
end;$$;
results (timings should probably be taken with a pinch of salt but each query is run twice to counter any caching)
first using the function we've written:
\timing on
--
select * from f(20000, 30000, 5) order by frequency desc limit 5;
/*
_id | word | frequency | lset | width_granule
-----+-----------+-----------+-------+---------------
141 | word23237 | 7092 | 23237 | 9
246 | word25112 | 4065 | 25112 | 8
275 | word23825 | 3636 | 23825 | 8
409 | word28660 | 2444 | 28660 | 8
418 | word29923 | 2392 | 29923 | 8
Time: 80.452 ms
*/
select * from f(20000, 30000, 5) order by frequency desc limit 5;
/*
_id | word | frequency | lset | width_granule
-----+-----------+-----------+-------+---------------
141 | word23237 | 7092 | 23237 | 9
246 | word25112 | 4065 | 25112 | 8
275 | word23825 | 3636 | 23825 | 8
409 | word28660 | 2444 | 28660 | 8
418 | word29923 | 2392 | 29923 | 8
Time: 0.510 ms
*/
and then with a simple index scan:
select * from lexikon where lset between 20000 and 30000 order by frequency desc limit 5;
/*
_id | word | frequency | lset | width_granule
-----+-----------+-----------+-------+---------------
141 | word23237 | 7092 | 23237 | 9
246 | word25112 | 4065 | 25112 | 8
275 | word23825 | 3636 | 23825 | 8
409 | word28660 | 2444 | 28660 | 8
418 | word29923 | 2392 | 29923 | 8
Time: 218.897 ms
*/
select * from lexikon where lset between 20000 and 30000 order by frequency desc limit 5;
/*
_id | word | frequency | lset | width_granule
-----+-----------+-----------+-------+---------------
141 | word23237 | 7092 | 23237 | 9
246 | word25112 | 4065 | 25112 | 8
275 | word23825 | 3636 | 23825 | 8
409 | word28660 | 2444 | 28660 | 8
418 | word29923 | 2392 | 29923 | 8
Time: 51.250 ms
*/
\timing off
--
rollback;
Depending on your real-world data, you will probably want to vary the number of granules and the function used for putting rows into them. The actual distribution of frequencies is key here, as is the expected values for the limit clause and size of lset ranges sought.
Setup
I am building on @Jack's setup to make it easier for people to follow and compare. Tested with PostgreSQL 9.1.4.
CREATE TABLE lexikon (
lex_id serial PRIMARY KEY
, word text
, frequency int NOT NULL -- we'd need to do more if NULL was allowed
, lset int
);
INSERT INTO lexikon(word, frequency, lset)
SELECT 'w' || g -- shorter with just 'w'
, (1000000 / row_number() OVER (ORDER BY random()))::int
, g
FROM generate_series(1,1000000) g
From here on I take a different route:
ANALYZE lexikon;
Auxiliary table
This solution does not add columns to the original table, it just needs a tiny helper table. I placed it in the schema public, use any schema of your choice.
CREATE TABLE public.lex_freq AS
WITH x AS (
SELECT DISTINCT ON (f.row_min)
f.row_min, c.row_ct, c.frequency
FROM (
SELECT frequency, sum(count(*)) OVER (ORDER BY frequency DESC) AS row_ct
FROM lexikon
GROUP BY 1
) c
JOIN ( -- list of steps in recursive search
VALUES (400),(1600),(6400),(25000),(100000),(200000),(400000),(600000),(800000)
) f(row_min) ON c.row_ct >= f.row_min -- match next greater number
ORDER BY f.row_min, c.row_ct, c.frequency DESC
)
, y AS (
SELECT DISTINCT ON (frequency)
row_min, row_ct, frequency AS freq_min
, lag(frequency) OVER (ORDER BY row_min) AS freq_max
FROM x
ORDER BY frequency, row_min
-- if one frequency spans multiple ranges, pick the lowest row_min
)
SELECT row_min, row_ct, freq_min
, CASE freq_min <= freq_max
WHEN TRUE THEN 'frequency >= ' || freq_min || ' AND frequency < ' || freq_max
WHEN FALSE THEN 'frequency = ' || freq_min
ELSE 'frequency >= ' || freq_min
END AS cond
FROM y
ORDER BY row_min;
Table looks like this:
row_min | row_ct | freq_min | cond
--------+---------+----------+-------------
400 | 400 | 2500 | frequency >= 2500
1600 | 1600 | 625 | frequency >= 625 AND frequency < 2500
6400 | 6410 | 156 | frequency >= 156 AND frequency < 625
25000 | 25000 | 40 | frequency >= 40 AND frequency < 156
100000 | 100000 | 10 | frequency >= 10 AND frequency < 40
200000 | 200000 | 5 | frequency >= 5 AND frequency < 10
400000 | 500000 | 2 | frequency >= 2 AND frequency < 5
600000 | 1000000 | 1 | frequency = 1
As the column cond is going to be used in dynamic SQL further down, you have to make this table secure. Always schema-qualify the table if you cannot be sure of an appropriate current search_path, and revoke write privileges from public (and any other untrusted role):
REVOKE ALL ON public.lex_freq FROM public;
GRANT SELECT ON public.lex_freq TO public;
The table lex_freq serves three purposes:
- Create needed partial indexes automatically.
- Provide steps for iterative function.
- Meta information for tuning.
Indexes
This DO statement creates all needed indexes:
DO
$$
DECLARE
_cond text;
BEGIN
FOR _cond IN
SELECT cond FROM public.lex_freq
LOOP
IF _cond LIKE 'frequency =%' THEN
EXECUTE 'CREATE INDEX ON lexikon(lset) WHERE ' || _cond;
ELSE
EXECUTE 'CREATE INDEX ON lexikon(lset, frequency DESC) WHERE ' || _cond;
END IF;
END LOOP;
END
$$
All of these partial indexes together span the table once. They are about the same size as one basic index on the whole table:
SELECT pg_size_pretty(pg_relation_size('lexikon')); -- 50 MB
SELECT pg_size_pretty(pg_total_relation_size('lexikon')); -- 71 MB
Only 21 MB of indexes for 50 MB table so far.
I create most of the partial indexes on (lset, frequency DESC). The second column only helps in special cases. But as both involved columns are of type integer, due to the specifics of data alignment in combination with MAXALIGN in PostgreSQL, the second column does not make the index any bigger. It's a small win for hardly any cost.
There is no point in doing that for partial indexes that only span a single frequency. Those are just on (lset). Created indexes look like this:
CREATE INDEX ON lexikon(lset, frequency DESC) WHERE frequency >= 2500;
CREATE INDEX ON lexikon(lset, frequency DESC) WHERE frequency >= 625 AND frequency < 2500;
-- ...
CREATE INDEX ON lexikon(lset, frequency DESC) WHERE frequency >= 2 AND frequency < 5;
CREATE INDEX ON lexikon(lset) WHERE freqency = 1;
Function
The function is somewhat similar in style to @Jack's solution:
CREATE OR REPLACE FUNCTION f_search(_lset_min int, _lset_max int, _limit int)
RETURNS SETOF lexikon
$func$
DECLARE
_n int;
_rest int := _limit; -- init with _limit param
_cond text;
BEGIN
FOR _cond IN
SELECT l.cond FROM public.lex_freq l ORDER BY l.row_min
LOOP
-- RAISE NOTICE '_cond: %, _limit: %', _cond, _rest; -- for debugging
RETURN QUERY EXECUTE '
SELECT *
FROM public.lexikon
WHERE ' || _cond || '
AND lset >= $1
AND lset <= $2
ORDER BY frequency DESC
LIMIT $3'
USING _lset_min, _lset_max, _rest;
GET DIAGNOSTICS _n = ROW_COUNT;
_rest := _rest - _n;
EXIT WHEN _rest < 1;
END LOOP;
END
$func$ LANGUAGE plpgsql STABLE;
Key differences:
dynamic SQL with
RETURN QUERY EXECUTE.
As we loop through the steps, a different query plan may be beneficiary. The query plan for static SQL is generated once and then reused - which can save some overhead. But in this case the query is simple and the values are very different. Dynamic SQL will be a big win.Dynamic
LIMITfor every query step.
This helps in multiple ways: First, rows are only fetched as needed. In combination with dynamic SQL this may also generate different query plans to begin with. Second: No need for an additionalLIMITin the function call to trim the surplus.
Benchmark
Setup
I picked four examples and ran three different tests with each. I took the best of five to compare with warm cache:
The raw SQL query of the form:
SELECT * FROM lexikon WHERE lset >= 20000 AND lset <= 30000 ORDER BY frequency DESC LIMIT 5;The same after creating this index
CREATE INDEX ON lexikon(lset);Needs about the same space as all my partial indexes together:
SELECT pg_size_pretty(pg_total_relation_size('lexikon')) -- 93 MBThe function
SELECT * FROM f_search(20000, 30000, 5);
Results
SELECT * FROM f_search(20000, 30000, 5);1: Total runtime: 315.458 ms
2: Total runtime: 36.458 ms
3: Total runtime: 0.330 ms
SELECT * FROM f_search(60000, 65000, 100);1: Total runtime: 294.819 ms
2: Total runtime: 18.915 ms
3: Total runtime: 1.414 ms
SELECT * FROM f_search(10000, 70000, 100);1: Total runtime: 426.831 ms
2: Total runtime: 217.874 ms
3: Total runtime: 1.611 ms
SELECT * FROM f_search(1, 1000000, 5);1: Total runtime: 2458.205 ms
2: Total runtime: 2458.205 ms -- for large ranges of lset, seq scan is faster than index.
3: Total runtime: 0.266 ms
Conclusion
As expected, the benefit from the function grows with bigger ranges of lset and smaller LIMIT.
With very small ranges of lset, the raw query in combination with the index is actually faster. You'll want to test and maybe branch: raw query for small ranges of lset, else function call. You could even just build that into the function for a "best of both worlds" - that's what I would do.
Depending on your data distribution and typical queries, more steps in lex_freq may help performance. Test to find the sweet spot. With the tools presented here, it should be easy to test.