How to speed up ORDER BY sorting when using GIN index in PostgreSQL?
I've done a lot of experimenting and here are my findings.

GIN and sorting

GIN index currently (as of version 9.4) can not assist ordering.


  Of the index types currently supported by PostgreSQL, only B-tree can produce sorted output — the other index types return matching rows in an unspecified, implementation-dependent order.


work_mem

Thanks Chris for pointing out to this configuration parameter.
It defaults to 4MB, and in case your recordset is larger, increasing work_mem to proper value (can be found from EXPLAIN ANALYSE) can significantly speed up sort operations.

ALTER SYSTEM SET work_mem TO '32MB';


Restart the server for change to take effect, then double check:

SHOW work_mem;


Original query

I've populated my database with 650k products with some categories holding up to 40k products. I've simplified query a bit by removing published clause:

SELECT * FROM products WHERE category_ids @&gt; ARRAY [248688]
ORDER BY score DESC, title LIMIT 10 OFFSET 30000;

Limit  (cost=2435.62..2435.62 rows=1 width=1390) (actual time=1141.254..1141.256 rows=10 loops=1)
  -&gt;  Sort  (cost=2434.00..2435.62 rows=646 width=1390) (actual time=1115.706..1140.513 rows=30010 loops=1)
        Sort Key: score, title
        Sort Method: external merge  Disk: 29656kB
        -&gt;  Bitmap Heap Scan on products  (cost=17.01..2403.85 rows=646 width=1390) (actual time=11.831..25.646 rows=41666 loops=1)
              Recheck Cond: (category_ids @&gt; '{248688}'::integer[])
              Heap Blocks: exact=6471
              -&gt;  Bitmap Index Scan on idx_products_category_ids_gin  (cost=0.00..16.85 rows=646 width=0) (actual time=10.140..10.140 rows=41666 loops=1)
                    Index Cond: (category_ids @&gt; '{248688}'::integer[])
Planning time: 0.288 ms
Execution time: 1146.322 ms


As we can see work_mem was not enough so we had Sort Method: external merge  Disk: 29656kB (the number here is approximate, it needs slightly more than 32MB for in-memory quicksort).

Reduce memory footprint

Don't select full records for sorting, use ids, apply sort, offset and limit, then load just 10 records we need:

SELECT * FROM products WHERE id in (
  SELECT id FROM products WHERE category_ids @&gt; ARRAY[248688]
  ORDER BY score DESC, title LIMIT 10 OFFSET 30000
) ORDER BY score DESC, title;

Sort  (cost=2444.10..2444.11 rows=1 width=1390) (actual time=707.861..707.862 rows=10 loops=1)
  Sort Key: products.score, products.title
  Sort Method: quicksort  Memory: 35kB
  -&gt;  Nested Loop  (cost=2436.05..2444.09 rows=1 width=1390) (actual time=707.764..707.803 rows=10 loops=1)
        -&gt;  HashAggregate  (cost=2435.63..2435.64 rows=1 width=4) (actual time=707.744..707.746 rows=10 loops=1)
              Group Key: products_1.id
              -&gt;  Limit  (cost=2435.62..2435.62 rows=1 width=72) (actual time=707.732..707.734 rows=10 loops=1)
                    -&gt;  Sort  (cost=2434.00..2435.62 rows=646 width=72) (actual time=704.163..706.955 rows=30010 loops=1)
                          Sort Key: products_1.score, products_1.title
                          Sort Method: quicksort  Memory: 7396kB
                          -&gt;  Bitmap Heap Scan on products products_1  (cost=17.01..2403.85 rows=646 width=72) (actual time=11.587..35.076 rows=41666 loops=1)
                                Recheck Cond: (category_ids @&gt; '{248688}'::integer[])
                                Heap Blocks: exact=6471
                                -&gt;  Bitmap Index Scan on idx_products_category_ids_gin  (cost=0.00..16.85 rows=646 width=0) (actual time=9.883..9.883 rows=41666 loops=1)
                                      Index Cond: (category_ids @&gt; '{248688}'::integer[])
        -&gt;  Index Scan using products_pkey on products  (cost=0.42..8.45 rows=1 width=1390) (actual time=0.004..0.004 rows=1 loops=10)
              Index Cond: (id = products_1.id)
Planning time: 0.682 ms
Execution time: 707.973 ms


Note Sort Method: quicksort  Memory: 7396kB. Result is much better.

JOIN and additional B-tree index

As Chris advised I've created additional index:

CREATE INDEX idx_test7 ON products (score DESC, title);


First I tried joining like this:

SELECT * FROM products NATURAL JOIN
  (SELECT id FROM products WHERE category_ids @&gt; ARRAY[248688]
  ORDER BY score DESC, title LIMIT 10 OFFSET 30000) c
ORDER BY score DESC, title;


Query plan differs slightly but result is the same:

Sort  (cost=2444.10..2444.11 rows=1 width=1390) (actual time=700.747..700.747 rows=10 loops=1)
  Sort Key: products.score, products.title
  Sort Method: quicksort  Memory: 35kB
  -&gt;  Nested Loop  (cost=2436.05..2444.09 rows=1 width=1390) (actual time=700.651..700.690 rows=10 loops=1)
        -&gt;  HashAggregate  (cost=2435.63..2435.64 rows=1 width=4) (actual time=700.630..700.630 rows=10 loops=1)
              Group Key: products_1.id
              -&gt;  Limit  (cost=2435.62..2435.62 rows=1 width=72) (actual time=700.619..700.619 rows=10 loops=1)
                    -&gt;  Sort  (cost=2434.00..2435.62 rows=646 width=72) (actual time=697.304..699.868 rows=30010 loops=1)
                          Sort Key: products_1.score, products_1.title
                          Sort Method: quicksort  Memory: 7396kB
                          -&gt;  Bitmap Heap Scan on products products_1  (cost=17.01..2403.85 rows=646 width=72) (actual time=10.796..32.258 rows=41666 loops=1)
                                Recheck Cond: (category_ids @&gt; '{248688}'::integer[])
                                Heap Blocks: exact=6471
                                -&gt;  Bitmap Index Scan on idx_products_category_ids_gin  (cost=0.00..16.85 rows=646 width=0) (actual time=9.234..9.234 rows=41666 loops=1)
                                      Index Cond: (category_ids @&gt; '{248688}'::integer[])
        -&gt;  Index Scan using products_pkey on products  (cost=0.42..8.45 rows=1 width=1390) (actual time=0.004..0.004 rows=1 loops=10)
              Index Cond: (id = products_1.id)
Planning time: 1.015 ms
Execution time: 700.918 ms


Playing with various offsets and product counts I could not make PostgreSQL use additional B-tree index.

So I went classical way and created junction table:

CREATE TABLE prodcats AS SELECT id AS product_id, unnest(category_ids) AS category_id FROM products;
CREATE INDEX idx_prodcats_cat_prod_id ON prodcats (category_id, product_id);

SELECT p.* FROM products p JOIN prodcats c ON (p.id=c.product_id)
WHERE c.category_id=248688
ORDER BY p.score DESC, p.title LIMIT 10 OFFSET 30000;

Limit  (cost=122480.06..122480.09 rows=10 width=1390) (actual time=1290.360..1290.362 rows=10 loops=1)
  -&gt;  Sort  (cost=122405.06..122509.00 rows=41574 width=1390) (actual time=1264.250..1289.575 rows=30010 loops=1)
        Sort Key: p.score, p.title
        Sort Method: external merge  Disk: 29656kB
        -&gt;  Merge Join  (cost=50.46..94061.13 rows=41574 width=1390) (actual time=117.746..182.048 rows=41666 loops=1)
              Merge Cond: (p.id = c.product_id)
              -&gt;  Index Scan using products_pkey on products p  (cost=0.42..90738.43 rows=646067 width=1390) (actual time=0.034..116.313 rows=210283 loops=1)
              -&gt;  Index Only Scan using idx_prodcats_cat_prod_id on prodcats c  (cost=0.43..1187.98 rows=41574 width=4) (actual time=0.022..7.137 rows=41666 loops=1)
                    Index Cond: (category_id = 248688)
                    Heap Fetches: 0
Planning time: 0.873 ms
Execution time: 1294.826 ms


Still not using B-tree index, resultset did not fit work_mem, hence poor results.

But under some circumstances, having large number of products and small offset PostgreSQL now decides to use B-tree index:

SELECT p.* FROM products p JOIN prodcats c ON (p.id=c.product_id)
WHERE c.category_id=248688
ORDER BY p.score DESC, p.title LIMIT 10 OFFSET 300;

Limit  (cost=3986.65..4119.51 rows=10 width=1390) (actual time=264.176..264.574 rows=10 loops=1)
  -&gt;  Nested Loop  (cost=0.98..552334.77 rows=41574 width=1390) (actual time=250.378..264.558 rows=310 loops=1)
        -&gt;  Index Scan using idx_test7 on products p  (cost=0.55..194665.62 rows=646067 width=1390) (actual time=0.030..83.026 rows=108037 loops=1)
        -&gt;  Index Only Scan using idx_prodcats_cat_prod_id on prodcats c  (cost=0.43..0.54 rows=1 width=4) (actual time=0.001..0.001 rows=0 loops=108037)
              Index Cond: ((category_id = 248688) AND (product_id = p.id))
              Heap Fetches: 0
Planning time: 0.585 ms
Execution time: 264.664 ms


This is in fact quite logical as B-tree index here does not produce direct result, it is only used as a guide for sequential scan.

Let's compare with GIN query:

SELECT * FROM products WHERE id in (
  SELECT id FROM products WHERE category_ids @&gt; ARRAY[248688]
  ORDER BY score DESC, title LIMIT 10 OFFSET 300
) ORDER BY score DESC, title;

Sort  (cost=2519.53..2519.55 rows=10 width=1390) (actual time=143.809..143.809 rows=10 loops=1)
  Sort Key: products.score, products.title
  Sort Method: quicksort  Memory: 35kB
  -&gt;  Nested Loop  (cost=2435.14..2519.36 rows=10 width=1390) (actual time=143.693..143.736 rows=10 loops=1)
        -&gt;  HashAggregate  (cost=2434.71..2434.81 rows=10 width=4) (actual time=143.678..143.680 rows=10 loops=1)
              Group Key: products_1.id
              -&gt;  Limit  (cost=2434.56..2434.59 rows=10 width=72) (actual time=143.668..143.670 rows=10 loops=1)
                    -&gt;  Sort  (cost=2433.81..2435.43 rows=646 width=72) (actual time=143.642..143.653 rows=310 loops=1)
                          Sort Key: products_1.score, products_1.title
                          Sort Method: top-N heapsort  Memory: 68kB
                          -&gt;  Bitmap Heap Scan on products products_1  (cost=17.01..2403.85 rows=646 width=72) (actual time=11.625..31.868 rows=41666 loops=1)
                                Recheck Cond: (category_ids @&gt; '{248688}'::integer[])
                                Heap Blocks: exact=6471
                                -&gt;  Bitmap Index Scan on idx_products_category_ids_gin  (cost=0.00..16.85 rows=646 width=0) (actual time=9.916..9.916 rows=41666 loops=1)
                                      Index Cond: (category_ids @&gt; '{248688}'::integer[])
        -&gt;  Index Scan using products_pkey on products  (cost=0.42..8.45 rows=1 width=1390) (actual time=0.004..0.004 rows=1 loops=10)
              Index Cond: (id = products_1.id)
Planning time: 0.630 ms
Execution time: 143.921 ms


GIN's result is much better. I checked with various combinations of number of products and offset, under no circumstances junction table approach was any better.

The power of real index

In order for PostgreSQL to fully utilize index for sorting, all query WHERE parameters
as well as ORDER BY parameters must reside in single B-tree index.
To do this I have copied sort fields from product to junction table:

CREATE TABLE prodcats AS SELECT id AS product_id, unnest(category_ids) AS category_id, score, title FROM products;
CREATE INDEX idx_prodcats_1 ON prodcats (category_id, score DESC, title, product_id);

SELECT * FROM products WHERE id in (SELECT product_id FROM prodcats WHERE category_id=248688 ORDER BY score DESC, title LIMIT 10 OFFSET 30000) ORDER BY score DESC, title;

Sort  (cost=2149.65..2149.67 rows=10 width=1390) (actual time=7.011..7.011 rows=10 loops=1)
  Sort Key: products.score, products.title
  Sort Method: quicksort  Memory: 35kB
  -&gt;  Nested Loop  (cost=2065.26..2149.48 rows=10 width=1390) (actual time=6.916..6.950 rows=10 loops=1)
        -&gt;  HashAggregate  (cost=2064.83..2064.93 rows=10 width=4) (actual time=6.902..6.904 rows=10 loops=1)
              Group Key: prodcats.product_id
              -&gt;  Limit  (cost=2064.02..2064.71 rows=10 width=74) (actual time=6.893..6.895 rows=10 loops=1)
                    -&gt;  Index Only Scan using idx_prodcats_1 on prodcats  (cost=0.56..2860.10 rows=41574 width=74) (actual time=0.010..6.173 rows=30010 loops=1)
                          Index Cond: (category_id = 248688)
                          Heap Fetches: 0
        -&gt;  Index Scan using products_pkey on products  (cost=0.42..8.45 rows=1 width=1390) (actual time=0.003..0.003 rows=1 loops=10)
              Index Cond: (id = prodcats.product_id)
Planning time: 0.318 ms
Execution time: 7.066 ms


And this is the worst scenario with large number of products in chosen category and large offset. When offset=300 execution time is just 0.5 ms.

Unfortunately maintaining such a junction table requires extra effort. It could be accomplished via indexed materialized views,
but that is only useful when your data updates rarely, cause refreshing such materialized view is quite a heavy operation.

So I am staying with GIN index so far, with increased work_mem and reduced memory footprint query.