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From: Alexandre Felipe <o.alexandre.felipe@gmail.com>
Date: Fri, 6 Feb 2026 10:52:01 +0000
Message-ID: <CAE8JnxM5GDEWdvEckjgG60OwPK04pZ9dSyxYm2+-PuyKCpmo-w@mail.gmail.com>
Subject: Re: New access method for b-tree.
To: "pgsql-hackers@postgresql.org" <pgsql-hackers@postgresql.org>, pt@bowt.ie, michael@paquier.xyz, 
	tgl@sss.pgh.pa.us, "peter@eisentraut.org" <peter@eisentraut.org>
Cc: Ants Aasma <ants.aasma@cybertec.at>, Tomas Vondra <tomas@vondra.me>, 
	Alexandre Felipe <alexandre.felipe@tpro.io>, =?UTF-8?B?TWljaGHFgiBLxYJlY3plaw==?= <michal@kleczek.org>, 
	pg@bowt.ie
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Hello again hackers!

+pt@bowt.ie <pt@bowt.ie>: That seems to be the one that is probably the
most familiar with the index scan (based on the commits).
+michael@paquier.xyz <michael@paquier.xyz> , +tgl@sss.pgh.pa.us
<tgl@sss.pgh.pa.us> , +peter@eisentraut.org <peter@eisentraut.org> as the
top 3 committers to nbtree over the last ~6 months.

I  have made substantial progress on adding a few features. I have
questions, but I will let you go first :)

Motivation:
*In technical terms:* this proposal is to take advantage of a btree index
when the query is filtered by a few distinct prefixes and ordered by a
suffix and has a limit.
*In non technical:* This could help to efficiently render a social network
feed, where each user can select a list of users whose posts they want to
see, and the posts must be ordered from newest to oldest.


*Performance Comparison*
I did a test with a toy table, please find more details below.

With limit 100

| Method     | Shared Hit | Shared Read | Exec Time |
|------------|-----------:|------------:|----------:|
| Merge      |         13 |         119 |     13 ms |
| IndexScan  |     15,308 |     525,310 |  3,409 ms |

With limit 1,000,000

| Method     |  SharedHit | SharRead | Temp I | Temp O | Exec Time |
|------------|-----------:|---------:|-------:|-------:|----------:|
| Merge      |    980,318 |   19,721 |      0 |      0 |  2,128 ms |
| Sequential |     15,208 |  525,410 | 20,207 | 35,384 |  3,762 ms |
| Bitmap     |        629 |  113,759 | 20,207 | 35,385 |  5,487 ms |
| IndexScan  |  7,880,619 |  126,706 | 20,945 | 35,386 |  5,874 ms |

Sequential scans and bitmap scans in this case reduces significantly the
number of
accessed buff because the table has only four integer columns, and these
methods
can read all the lines on a given page at a time.

However that comes at the cost of resorting to an in-disk sort method.
For the query with limit 100 we get no temp files as we are using a
top-100 sort.

make check passes


*Experiment details*

Consider a 100M row table formed (a,b,c,d) \in 100 x 100 x 100 x 100


```sql
CREATE TABLE grid AS (
    SELECT a, b, c, d, FROM
        generate_series(1, 100) AS a,
        generate_series(1, 100) AS b,
        generate_series(1, 100) AS c,
        generate_series(1, 100) AS d
);

CREATE INDEX grid_index ON grid (a, b, c);
ANALYSE grid;
```

Now let's say that we need to find certain number of rows filtered by a and
ordered by b;
```sql
PREPARE grid_query(int) AS
SELECT sum(d) FROM (
    SELECT * FROM grid
    WHERE a IN (2,3,5,8,13,21,34,55) AND b >=3D 0
    ORDER BY b
    LIMIT $1) t;
```

---


Now with limit 100, with index merge scan (notice Index Prefixes in the
plan).

```sql
SET enable_indexmergescan =3D on;
EXPLAIN (ANALYSE) EXECUTE grid_query(100);
```

```text
   Buffers: shared hit=3D13 read=3D119
   ->  Limit  (cost=3D0.57..87.29 rows=3D100 width=3D16) (actual
time=3D5.528..12.999 rows=3D100.00 loops=3D1)
         Buffers: shared hit=3D13 read=3D119
         ->  Index Scan using grid_a_b_c_idx on grid  (cost=3D0.57..93.36
rows=3D107 width=3D16) (actual time=3D5.528..12.994 rows=3D100.00 loops=3D1=
)
               Index Cond: (b >=3D 0)
               *Index Prefixes: *(a =3D ANY
('{2,3,5,8,13,21,34,55}'::integer[]))
               Index Searches: 8
               Buffers: shared hit=3D13 read=3D119
 Planning:
   Buffers: shared hit=3D59 read=3D23
 Planning Time: 4.619 ms
 Execution Time: 13.055 ms
 ```


```sql
SET enable_indexmergescan =3D off;
EXPLAIN (ANALYSE) EXECUTE grid_query(100);
```

```text
 Aggregate  (cost=3D1603588.06..1603588.07 rows=3D1 width=3D8) (actual
time=3D3406.624..3408.710 rows=3D1.00 loops=3D1)
   Buffers: shared hit=3D15308 read=3D525310
   ->  Limit  (cost=3D1603575.17..1603586.81 rows=3D100 width=3D16) (actual
time=3D3406.601..3408.702 rows=3D100.00 loops=3D1)
         Buffers: shared hit=3D15308 read=3D525310
         ->  Gather Merge  (cost=3D1603575.17..2514342.92 rows=3D7819999
width=3D16) (actual time=3D3406.598..3408.695 rows=3D100.00 loops=3D1)
               Workers Planned: 2
               Workers Launched: 2
               Buffers: shared hit=3D15308 read=3D525310
               ->  Sort  (cost=3D1602575.14..1610720.98 rows=3D3258333
width=3D16) (actual time=3D3393.782..3393.784 rows=3D100.00 loops=3D3)
                     Sort Key: grid.b
                     Sort Method: top-N heapsort  Memory: 32kB
                     Buffers: shared hit=3D15308 read=3D525310
                     Worker 0:  Sort Method: top-N heapsort  Memory: 32kB
                     Worker 1:  Sort Method: top-N heapsort  Memory: 32kB
                     ->  *Parallel Seq Scan* on grid
 (cost=3D0.00..1478044.00 rows=3D3258333 width=3D16) (actual time=3D0.944..=
3129.896
rows=3D2666666.67 loops=3D3)
                           Filter: ((b >=3D 0) AND (a =3D ANY
('{2,3,5,8,13,21,34,55}'::integer[])))
                           Rows Removed by Filter: 30666667
                           Buffers: shared hit=3D15234 read=3D525310
 Planning Time: 0.370 ms
 Execution Time: 3409.134 ms
 ```

Now queries with limit 1,000,000

```sql
SET enable_indexmergescan =3D on;
EXPLAIN ANALYSE EXECUTE grid_query(1000000);
```

Query executed with the proposed access method. Notice in the plan Index
Prefixes and Index Cond.
```text
   Buffers: shared hit=3D980318 read=3D19721
   ->  Limit  (cost=3D0.57..867259.84 rows=3D1000000 width=3D16) (actual
time=3D2.854..2103.438 rows=3D1000000.00 loops=3D1)
         Buffers: shared hit=3D980318 read=3D19721
         ->  Index Scan using grid_a_b_c_idx on grid  (cost=3D0.57..867265.=
91
rows=3D1000007 width=3D16) (actual time=3D2.852..2066.205 rows=3D1000000.00=
 loops=3D1)
               Index Cond: (b >=3D 0)
               *Index Prefixes:* (a =3D ANY
('{2,3,5,8,13,21,34,55}'::integer[]))
               Index Searches: 8
               Buffers: shared hit=3D980318 read=3D19721
 Planning Time: 0.328 ms
 Execution Time: 2127.811 ms
 ```

If we disable index_mergescan we naturally we fall into a sequential scan.

```sql
SET enable_indexmergescan =3D off;
EXPLAIN ANALYSE EXECUTE grid_query(1000000);
```
```text
   Buffers: shared hit=3D15208 read=3D525410, temp read=3D20207 written=3D3=
5384
   ->  Limit  (cost=3D1942895.64..2059362.12 rows=3D1000000 width=3D16) (ac=
tual
time=3D3467.012..3712.044 rows=3D1000000.00 loops=3D1)
         Buffers: shared hit=3D15208 read=3D525410, temp read=3D20207
written=3D35384
         ->  Gather Merge  (cost=3D1942895.64..2853663.39 rows=3D7819999
width=3D16) (actual time=3D3467.010..3671.220 rows=3D1000000.00 loops=3D1)
               Workers Planned: 2
               Workers Launched: 2
               Buffers: shared hit=3D15208 read=3D525410, temp read=3D20207
written=3D35384
               ->  Sort  (cost=3D1941895.62..1950041.45 rows=3D3258333
width=3D16) (actual time=3D3455.852..3476.358 rows=3D334576.33 loops=3D3)
                     Sort Key: grid.b
                     Sort Method: *external merge  Disk: 47016kB*
                     Buffers: shared hit=3D15208 read=3D525410, temp read=
=3D20207
written=3D35384
                     Worker 0:  Sort Method: external merge  Disk: 46976kB
                     Worker 1:  Sort Method: external merge  Disk: 47000kB
                     ->  *Parallel Seq Scan* on grid
 (cost=3D0.00..1478044.00 rows=3D3258333 width=3D16) (actual time=3D2.789..=
2779.483
rows=3D2666666.67 loops=3D3)
                           Filter: ((b >=3D 0) AND (a =3D ANY
('{2,3,5,8,13,21,34,55}'::integer[])))
                           Rows Removed by Filter: 30666667
                           Buffers: shared hit=3D15134 read=3D525410
 Planning Time: 0.332 ms
 Execution Time: 3761.866 ms
```

If we disable sequential scans, then we get a bitmap scan

```sql
SET enable_seqscan =3D off;
EXPLAIN ANALYSE EXECUTE grid_query(1000000);
```
```text
   Buffers: shared hit=3D629 read=3D113759 written=3D2, temp read=3D20207
written=3D35385
   ->  Limit  (cost=3D1998199.78..2114666.26 rows=3D1000000 width=3D16) (ac=
tual
time=3D5170.456..5453.433 rows=3D1000000.00 loops=3D1)
         Buffers: shared hit=3D629 read=3D113759 written=3D2, temp read=3D2=
0207
written=3D35385
         ->  Gather Merge  (cost=3D1998199.78..2908967.53 rows=3D7819999
width=3D16) (actual time=3D5170.455..5413.254 rows=3D1000000.00 loops=3D1)
               Workers Planned: 2
               Workers Launched: 2
               Buffers: shared hit=3D629 read=3D113759 written=3D2, temp
read=3D20207 written=3D35385
               ->  Sort  (cost=3D1997199.75..2005345.59 rows=3D3258333
width=3D16) (actual time=3D5156.929..5177.507 rows=3D334500.67 loops=3D3)
                     Sort Key: grid.b
                     Sort Method: external merge  Disk: 47032kB
                     Buffers: shared hit=3D629 read=3D113759 written=3D2, t=
emp
read=3D20207 written=3D35385
                     Worker 0:  Sort Method: external merge  Disk: 47280kB
                     Worker 1:  Sort Method: external merge  Disk: 46680kB
                     ->  Parallel Bitmap Heap Scan on grid
 (cost=3D107691.54..1533348.13 rows=3D3258333 width=3D16) (actual
time=3D299.891..4489.787 rows=3D2666666.67 loops=3D3)
                           Recheck Cond: ((a =3D ANY
('{2,3,5,8,13,21,34,55}'::integer[])) AND (b >=3D 0))
                           Rows *Removed by Index Recheck*: 2410242
                           Heap Blocks: exact=3D13100 lossy=3D22639
                           Buffers: shared hit=3D615 read=3D113759 written=
=3D2
                           Worker 0:  Heap Blocks: exact=3D13077 lossy=3D22=
755
                           Worker 1:  Heap Blocks: exact=3D13036 lossy=3D22=
421
                           ->  *Bitmap Index Scan* on grid_a_b_c_idx
 (cost=3D0.00..105736.54 rows=3D7820000 width=3D0) (actual time=3D297.651..=
297.651
rows=3D8000000.00 loops=3D1)
                                 Index Cond: ((a =3D ANY
('{2,3,5,8,13,21,34,55}'::integer[])) AND (b >=3D 0))
                                 Index Searches: 7
                                 Buffers: shared hit=3D13 read=3D7293 writt=
en=3D2
 Planning Time: 0.165 ms
 Execution Time: 5487.213 ms
```

If we disable bitmap scans we finally get an index scan

```sql
SET enable_bitmapscan =3D off;
EXPLAIN ANALYSE EXECUTE grid_query(1000000);
```
```
   Buffers: shared hit=3D7883221 read=3D124111, temp read=3D20699 written=
=3D35385
   ->  Limit  (cost=3D7201203.08..7317669.55 rows=3D1000000 width=3D16) (ac=
tual
time=3D4414.478..4674.400 rows=3D1000000.00 loops=3D1)
         Buffers: shared hit=3D7883221 read=3D124111, temp read=3D20699
written=3D35385
         ->  Gather Merge  (cost=3D7201203.08..8111970.83 rows=3D7819999
width=3D16) (actual time=3D4414.476..4633.982 rows=3D1000000.00 loops=3D1)
               Workers Planned: 2
               Workers Launched: 2
               Buffers: shared hit=3D7883221 read=3D124111, temp read=3D206=
99
written=3D35385
               ->  Sort  (cost=3D7200203.05..7208348.88 rows=3D3258333
width=3D16) (actual time=3D4390.625..4411.896 rows=3D334567.00 loops=3D3)
                     Sort Key: grid.b
                     Sort Method: *external merge  Disk: 47304kB*
                     Buffers: shared hit=3D7883221 read=3D124111, temp
read=3D20699 written=3D35385
                     Worker 0:  Sort Method: external merge  Disk: 47304kB
                     Worker 1:  Sort Method: external merge  Disk: 46384kB
                     ->  *Parallel Index Scan* using grid_a_b_c_idx on grid
 (cost=3D0.57..6736351.43 rows=3D3258333 width=3D16) (actual
time=3D46.925..3796.915 rows=3D2666666.67 loops=3D3)
                           Index Cond: ((a =3D ANY
('{2,3,5,8,13,21,34,55}'::integer[])) AND (b >=3D 0))
                           Index Searches: 7
                           Buffers: shared hit=3D7883208 read=3D124110
 Planning Time: 0.385 ms
 Execution Time: 4713.325 ms
 ```


On Thu, Feb 5, 2026 at 6:59=E2=80=AFAM Alexandre Felipe <
o.alexandre.felipe@gmail.com> wrote:

> Thank you for looking into this.
>
> Now we can execute a, still narrow, family queries!
>
> Maybe it helps to see this as a *social network feeds*. Imagine a social
> network, you have a few friends, or follow a few people, and you want to
> see their updates ordered by date. For each user we have a different
> combination of users that we have to display. But maybe, even having
> hundreds of users we will only show the first 10.
>
> There is a low hanging fruit on the skip scan, if we need N rows, and one
> group already has M rows we could stop there.
> If Nx is the number of friends, and M is the number of posts to show.
> This runs with complexity (Nx * M) rows, followed by an (Nx * M) sort,
> instead of (Nx * N) followed by an (Nx * N) sort.
> Where M =3D 10 and N is 1000 this is a significant improvement.
> But if M ~ N, the merge scan that runs with M + Nx row accesses, (M + Nx)
> heap operations.
> If everything is on the same page the skip scan would win.
>
> The cost estimation is probably far off.
> I am also not considering the filters applied after this operator, and I
> don't know if the planner infrastructure is able to adjust it by itself.
> This is where I would like reviewer's feedback. I think that the planner
> costs are something to be determined experimentally.
>
> Next I will make it slightly more general handling
> * More index columns: Index (a, b, s...) could support WHERE a IN (...)
> ORDER BY b LIMIT N (ignoring s...)
> * Multi-column prefix: WHERE (a, b) IN (...) ORDER BY c
> * Non-leading prefix: WHERE b IN (...) AND a =3D const ORDER BY c on inde=
x
> (a, b, c)
>
> ---
> Kind Regards,
> Alexandre
>
> On Wed, Feb 4, 2026 at 7:13=E2=80=AFAM Micha=C5=82 K=C5=82eczek <michal@k=
leczek.org> wrote:
>
>>
>>
>> On 3 Feb 2026, at 22:42, Ants Aasma <ants.aasma@cybertec.at> wrote:
>>
>> On Mon, 2 Feb 2026 at 01:54, Tomas Vondra <tomas@vondra.me> wrote:
>>
>> I'm also wondering how common is the targeted query pattern? How common
>> it is to have an IN condition on the leading column in an index, and
>> ORDER BY on the second one?
>>
>>
>> I have seen this pattern multiple times. My nickname for it is the
>> timeline view. Think of the social media timeline, showing posts from
>> all followed accounts in timestamp order, returned in reasonably sized
>> batches. The naive SQL query will have to scan all posts from all
>> followed accounts and pass them through a top-N sort. When the total
>> number of posts is much larger than the batch size this is much slower
>> than what is proposed here (assuming I understand it correctly) -
>> effectively equivalent to running N index scans through Merge Append.
>>
>>
>> My workarounds I have proposed users have been either to rewrite the
>> query as a UNION ALL of a set of single value prefix queries wrapped
>> in an order by limit. This gives the exact needed merge append plan
>> shape. But repeating the query N times can get unwieldy when the
>> number of values grows, so the fallback is:
>>
>> SELECT * FROM unnest(:friends) id, LATERAL (
>>    SELECT * FROM posts
>>    WHERE user_id =3D id
>>    ORDER BY tstamp DESC LIMIT 100)
>> ORDER BY tstamp DESC LIMIT 100;
>>
>> The downside of this formulation is that we still have to fetch a
>> batch worth of items from scans where we otherwise would have only had
>> to look at one index tuple.
>>
>>
>> GIST can be used to handle this kind of queries as it supports multiple
>> sort orders.
>> The only problem is that GIST does not support ORDER BY column.
>> One possible workaround is [1] but as described there it does not play
>> well with partitioning.
>> I=E2=80=99ve started drafting support for ORDER BY column in GIST - see =
[2].
>> I think it would be easier to implement and maintain than a new IAM (but
>> I don=E2=80=99t have enough knowledge and experience to implement it mys=
elf)
>>
>> [1]
>> https://www.postgresql.org/message-id/3FA1E0A9-8393-41F6-88BD-62EEEA1EC2=
1F%40kleczek.org
>> [2]
>> https://www.postgresql.org/message-id/B2AC13F9-6655-4E27-BFD3-068844E5DC=
91%40kleczek.org
>>
>> =E2=80=94
>> Kind regards,
>> Michal
>>
>

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<div dir=3D"ltr"><div dir=3D"ltr"><div dir=3D"ltr"><div>Hello again hackers=
!</div><br><div><a class=3D"gmail_plusreply" id=3D"m_1178963958729505245gma=
il-plusReplyChip-0" href=3D"mailto:pt@bowt.ie" target=3D"_blank">+pt@bowt.i=
e</a>: That seems to be the one that is probably the most familiar with the=
 index scan (based on the commits).</div><div><a class=3D"gmail_plusreply" =
id=3D"m_1178963958729505245gmail-plusReplyChip-2" href=3D"mailto:michael@pa=
quier.xyz" target=3D"_blank">+michael@paquier.xyz</a>=C2=A0,=C2=A0<a class=
=3D"gmail_plusreply" id=3D"m_1178963958729505245gmail-plusReplyChip-4" href=
=3D"mailto:tgl@sss.pgh.pa.us" target=3D"_blank">+tgl@sss.pgh.pa.us</a>=C2=
=A0,=C2=A0<a class=3D"gmail_plusreply" id=3D"m_1178963958729505245gmail-plu=
sReplyChip-5" href=3D"mailto:peter@eisentraut.org" target=3D"_blank">+peter=
@eisentraut.org</a>=C2=A0as the top 3 committers to nbtree over the last ~6=
 months.<br></div><div><br></div><div>I=C2=A0 have made substantial=C2=A0pr=
ogress on adding a few features. I have questions, but I will let you go fi=
rst :)</div><div><br></div><div><font size=3D"4">Motivation</font>:</div><d=
iv><b>In technical terms:</b> this proposal is to take advantage of a btree=
 index when the query is filtered by a few distinct prefixes and ordered by=
 a suffix and has a limit.<br></div><div><b>In non technical:</b> This coul=
d help to efficiently render=C2=A0a social network feed, where each user ca=
n select a list of users whose posts they want to see, and the posts must b=
e ordered from newest to oldest.</div><div><br></div><div><b><font size=3D"=
4">Performance Comparison</font><br></b><br>I did a test with a toy table, =
please find more details below.<br><br>With limit 100<br><br><font face=3D"=
monospace">| Method =C2=A0 =C2=A0 | Shared Hit | Shared Read | Exec Time |<=
br>|------------|-----------:|------------:|----------:|<br>| Merge =C2=A0 =
=C2=A0 =C2=A0| =C2=A0 =C2=A0 =C2=A0 =C2=A0 13 | =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 119 | =C2=A0 =C2=A0 13 ms |<br>| IndexScan =C2=A0| =C2=A0 =C2=A0 15,308 | =
=C2=A0 =C2=A0 525,310 | =C2=A03,409 ms |</font><br><br>With limit 1,000,000=
<br><br><font face=3D"monospace">| Method =C2=A0 =C2=A0 | =C2=A0SharedHit |=
 SharRead | Temp I | Temp O | Exec Time |<br>|------------|-----------:|---=
------:|-------:|-------:|----------:|<br>| Merge =C2=A0 =C2=A0 =C2=A0| =C2=
=A0 =C2=A0980,318 | =C2=A0 19,721 | =C2=A0 =C2=A0 =C2=A00 | =C2=A0 =C2=A0 =
=C2=A00 | =C2=A02,128 ms |<br>| Sequential | =C2=A0 =C2=A0 15,208 | =C2=A05=
25,410 | 20,207 | 35,384 | =C2=A03,762 ms |<br>| Bitmap =C2=A0 =C2=A0 | =C2=
=A0 =C2=A0 =C2=A0 =C2=A0629 | =C2=A0113,759 | 20,207 | 35,385 | =C2=A05,487=
 ms |<br>| IndexScan =C2=A0| =C2=A07,880,619 | =C2=A0126,706 | 20,945 | 35,=
386 | =C2=A05,874 ms |</font><br><br>Sequential scans and bitmap scans in t=
his case reduces significantly the number of <br>accessed buff because the =
table has only four integer columns, and these methods <br>can read all the=
 lines on a given page at a time.<br><br>However that comes at the cost of =
resorting to an in-disk sort method. <br>For the query with limit 100 we ge=
t no temp files as we are using a<br>top-100 sort.</div><div><br></div><div=
>make check passes</div><div><br><br><b><font size=3D"4">Experiment details=
</font></b><br><br>Consider a 100M row table formed (a,b,c,d) \in 100 x 100=
 x 100 x 100 <br><br><br>```sql<br><font face=3D"monospace">CREATE TABLE gr=
id AS (<br>=C2=A0 =C2=A0 SELECT a, b, c, d, FROM <br>=C2=A0 =C2=A0 =C2=A0 =
=C2=A0 generate_series(1, 100) AS a, <br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 genera=
te_series(1, 100) AS b, <br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 generate_series(1, =
100) AS c, <br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 generate_series(1, 100) AS d<br>=
);<br><br>CREATE INDEX grid_index ON grid (a, b, c);<br>ANALYSE grid;</font=
><br>```<br><br>Now let&#39;s say that we need to find certain number of ro=
ws filtered by a and ordered by b;<br>```sql<br><font face=3D"monospace">PR=
EPARE grid_query(int) AS<br>SELECT sum(d) FROM (<br>=C2=A0 =C2=A0 SELECT * =
FROM grid <br>=C2=A0 =C2=A0 WHERE a IN (2,3,5,8,13,21,34,55) AND b &gt;=3D =
0 <br>=C2=A0 =C2=A0 ORDER BY b <br>=C2=A0 =C2=A0 LIMIT $1) t;</font><br>```=
<br><br>---<br><br><br>Now with limit 100, with index merge scan (notice In=
dex Prefixes in the plan).<br><br>```sql<br>SET enable_indexmergescan =3D o=
n;<br>EXPLAIN (ANALYSE) EXECUTE grid_query(100);<br>```<br><br>```text<br>=
=C2=A0 =C2=A0Buffers: shared hit=3D13 read=3D119<br>=C2=A0 =C2=A0-&gt; =C2=
=A0Limit =C2=A0(cost=3D0.57..87.29 rows=3D100 width=3D16) (actual time=3D5.=
528..12.999 rows=3D100.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0B=
uffers: shared hit=3D13 read=3D119<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&g=
t; =C2=A0Index Scan using grid_a_b_c_idx on grid =C2=A0(cost=3D0.57..93.36 =
rows=3D107 width=3D16) (actual time=3D5.528..12.994 rows=3D100.00 loops=3D1=
)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Index Cond: (b =
&gt;=3D 0)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0<b>Ind=
ex Prefixes: </b>(a =3D ANY (&#39;{2,3,5,8,13,21,34,55}&#39;::integer[]))<b=
r>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Index Searches: 8<=
br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared h=
it=3D13 read=3D119<br>=C2=A0Planning:<br>=C2=A0 =C2=A0Buffers: shared hit=
=3D59 read=3D23<br>=C2=A0Planning Time: 4.619 ms<br>=C2=A0Execution Time: 1=
3.055 ms<br>=C2=A0```<br><br><br>```sql<br>SET enable_indexmergescan =3D of=
f;<br>EXPLAIN (ANALYSE) EXECUTE grid_query(100);<br>```<br><br>```text<br>=
=C2=A0Aggregate =C2=A0(cost=3D1603588.06..1603588.07 rows=3D1 width=3D8) (a=
ctual time=3D3406.624..3408.710 rows=3D1.00 loops=3D1)<br>=C2=A0 =C2=A0Buff=
ers: shared hit=3D15308 read=3D525310<br>=C2=A0 =C2=A0-&gt; =C2=A0Limit =C2=
=A0(cost=3D1603575.17..1603586.81 rows=3D100 width=3D16) (actual time=3D340=
6.601..3408.702 rows=3D100.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0Buffers: shared hit=3D15308 read=3D525310<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0-&gt; =C2=A0Gather Merge =C2=A0(cost=3D1603575.17..2514342.92 rows=
=3D7819999 width=3D16) (actual time=3D3406.598..3408.695 rows=3D100.00 loop=
s=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Workers Pl=
anned: 2<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Workers =
Launched: 2<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffe=
rs: shared hit=3D15308 read=3D525310<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0-&gt; =C2=A0Sort =C2=A0(cost=3D1602575.14..1610720.98 r=
ows=3D3258333 width=3D16) (actual time=3D3393.782..3393.784 rows=3D100.00 l=
oops=3D3)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0Sort Key: grid.b<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Sort Method: top-N heapsort =C2=A0Memory=
: 32kB<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0Buffers: shared hit=3D15308 read=3D525310<br>=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Worker 0: =C2=A0=
Sort Method: top-N heapsort =C2=A0Memory: 32kB<br>=C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Worker 1: =C2=A0Sort Me=
thod: top-N heapsort =C2=A0Memory: 32kB<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =C2=A0<b>Parallel Seq Sc=
an</b> on grid =C2=A0(cost=3D0.00..1478044.00 rows=3D3258333 width=3D16) (a=
ctual time=3D0.944..3129.896 rows=3D2666666.67 loops=3D3)<br>=C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0Filter: ((b &gt;=3D 0) AND (a =3D ANY (&#39;{2,3,5,8,13,21,34,55}=
&#39;::integer[])))<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Rows Removed by Filter: 306666=
67<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared hit=3D15234 read=3D525310<br>=
=C2=A0Planning Time: 0.370 ms<br>=C2=A0Execution Time: 3409.134 ms<br>=C2=
=A0```<br><br>Now queries with limit 1,000,000<br><br>```sql<br>SET enable_=
indexmergescan =3D on;<br>EXPLAIN ANALYSE EXECUTE grid_query(1000000);<br>`=
``<br><br>Query executed with the proposed access method. Notice in the pla=
n Index Prefixes and Index Cond.<br>```text<br>=C2=A0 =C2=A0Buffers: shared=
 hit=3D980318 read=3D19721<br>=C2=A0 =C2=A0-&gt; =C2=A0Limit =C2=A0(cost=3D=
0.57..867259.84 rows=3D1000000 width=3D16) (actual time=3D2.854..2103.438 r=
ows=3D1000000.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: s=
hared hit=3D980318 read=3D19721<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =
=C2=A0Index Scan using grid_a_b_c_idx on grid =C2=A0(cost=3D0.57..867265.91=
 rows=3D1000007 width=3D16) (actual time=3D2.852..2066.205 rows=3D1000000.0=
0 loops=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Inde=
x Cond: (b &gt;=3D 0)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0<b>Index Prefixes:</b> (a =3D ANY (&#39;{2,3,5,8,13,21,34,55}&#39;::i=
nteger[]))<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Index =
Searches: 8<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffe=
rs: shared hit=3D980318 read=3D19721<br>=C2=A0Planning Time: 0.328 ms<br>=
=C2=A0Execution Time: 2127.811 ms<br>=C2=A0```<br><br>If we disable index_m=
ergescan we naturally we fall into a sequential scan.<br><br>```sql<br>SET =
enable_indexmergescan =3D off;<br>EXPLAIN ANALYSE EXECUTE grid_query(100000=
0);<br>```<br>```text<br>=C2=A0 =C2=A0Buffers: shared hit=3D15208 read=3D52=
5410, temp read=3D20207 written=3D35384<br>=C2=A0 =C2=A0-&gt; =C2=A0Limit =
=C2=A0(cost=3D1942895.64..2059362.12 rows=3D1000000 width=3D16) (actual tim=
e=3D3467.012..3712.044 rows=3D1000000.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0Buffers: shared hit=3D15208 read=3D525410, temp read=3D20207 =
written=3D35384<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =C2=A0Gather Mer=
ge =C2=A0(cost=3D1942895.64..2853663.39 rows=3D7819999 width=3D16) (actual =
time=3D3467.010..3671.220 rows=3D1000000.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Workers Planned: 2<br>=C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Workers Launched: 2<br>=C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared hit=3D15208 re=
ad=3D525410, temp read=3D20207 written=3D35384<br>=C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =C2=A0Sort =C2=A0(cost=3D1941895.62..1=
950041.45 rows=3D3258333 width=3D16) (actual time=3D3455.852..3476.358 rows=
=3D334576.33 loops=3D3)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0 =C2=A0 =C2=A0Sort Key: grid.b<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Sort Method: <b>external m=
erge =C2=A0Disk: 47016kB</b><br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared hit=3D15208 read=3D525410=
, temp read=3D20207 written=3D35384<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Worker 0: =C2=A0Sort Method: exter=
nal merge =C2=A0Disk: 46976kB<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Worker 1: =C2=A0Sort Method: external mer=
ge =C2=A0Disk: 47000kB<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =C2=A0<b>Parallel Seq Scan</b> on grid =C2=
=A0(cost=3D0.00..1478044.00 rows=3D3258333 width=3D16) (actual time=3D2.789=
..2779.483 rows=3D2666666.67 loops=3D3)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Filter: (=
(b &gt;=3D 0) AND (a =3D ANY (&#39;{2,3,5,8,13,21,34,55}&#39;::integer[])))=
<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0Rows Removed by Filter: 30666667<br>=C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0Buffers: shared hit=3D15134 read=3D525410<br>=C2=A0Planning Ti=
me: 0.332 ms<br>=C2=A0Execution Time: 3761.866 ms<br>```<br>=C2=A0<br>If we=
 disable sequential scans, then we get a bitmap scan<br><br>```sql<br>SET e=
nable_seqscan =3D off;<br>EXPLAIN ANALYSE EXECUTE grid_query(1000000);<br>`=
``<br>```text<br>=C2=A0 =C2=A0Buffers: shared hit=3D629 read=3D113759 writt=
en=3D2, temp read=3D20207 written=3D35385<br>=C2=A0 =C2=A0-&gt; =C2=A0Limit=
 =C2=A0(cost=3D1998199.78..2114666.26 rows=3D1000000 width=3D16) (actual ti=
me=3D5170.456..5453.433 rows=3D1000000.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0Buffers: shared hit=3D629 read=3D113759 written=3D2, temp =
read=3D20207 written=3D35385<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =C2=
=A0Gather Merge =C2=A0(cost=3D1998199.78..2908967.53 rows=3D7819999 width=
=3D16) (actual time=3D5170.455..5413.254 rows=3D1000000.00 loops=3D1)<br>=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Workers Planned: 2<b=
r>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Workers Launched: =
2<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared=
 hit=3D629 read=3D113759 written=3D2, temp read=3D20207 written=3D35385<br>=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =C2=A0Sort =C2=
=A0(cost=3D1997199.75..2005345.59 rows=3D3258333 width=3D16) (actual time=
=3D5156.929..5177.507 rows=3D334500.67 loops=3D3)<br>=C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Sort Key: grid.b<br>=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0Sort Method: external merge =C2=A0Disk: 47032kB<br>=C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared hit=
=3D629 read=3D113759 written=3D2, temp read=3D20207 written=3D35385<br>=C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Wo=
rker 0: =C2=A0Sort Method: external merge =C2=A0Disk: 47280kB<br>=C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Worker 1:=
 =C2=A0Sort Method: external merge =C2=A0Disk: 46680kB<br>=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =C2=A0Para=
llel Bitmap Heap Scan on grid =C2=A0(cost=3D107691.54..1533348.13 rows=3D32=
58333 width=3D16) (actual time=3D299.891..4489.787 rows=3D2666666.67 loops=
=3D3)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Recheck Cond: ((a =3D ANY (&#39;{2,3,5,8,13,=
21,34,55}&#39;::integer[])) AND (b &gt;=3D 0))<br>=C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Ro=
ws <b>Removed by Index Recheck</b>: 2410242<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Heap B=
locks: exact=3D13100 lossy=3D22639<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shar=
ed hit=3D615 read=3D113759 written=3D2<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Worker 0:=
 =C2=A0Heap Blocks: exact=3D13077 lossy=3D22755<br>=C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Wo=
rker 1: =C2=A0Heap Blocks: exact=3D13036 lossy=3D22421<br>=C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0-&gt; =C2=A0<b>Bitmap Index Scan</b> on grid_a_b_c_idx =C2=A0(cost=3D=
0.00..105736.54 rows=3D7820000 width=3D0) (actual time=3D297.651..297.651 r=
ows=3D8000000.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0Index Cond: ((a =3D ANY (&#39;{2,3,5,8,13,21,34,55}&#39;::integer[])) AN=
D (b &gt;=3D 0))<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Index Search=
es: 7<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared hit=3D1=
3 read=3D7293 written=3D2<br>=C2=A0Planning Time: 0.165 ms<br>=C2=A0Executi=
on Time: 5487.213 ms<br>```<br><br>If we disable bitmap scans we finally ge=
t an index scan<br><br>```sql<br>SET enable_bitmapscan =3D off;<br>EXPLAIN =
ANALYSE EXECUTE grid_query(1000000);<br>```<br>```<br>=C2=A0 =C2=A0Buffers:=
 shared hit=3D7883221 read=3D124111, temp read=3D20699 written=3D35385<br>=
=C2=A0 =C2=A0-&gt; =C2=A0Limit =C2=A0(cost=3D7201203.08..7317669.55 rows=3D=
1000000 width=3D16) (actual time=3D4414.478..4674.400 rows=3D1000000.00 loo=
ps=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffers: shared hit=3D7883221 =
read=3D124111, temp read=3D20699 written=3D35385<br>=C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0-&gt; =C2=A0Gather Merge =C2=A0(cost=3D7201203.08..8111970.83 =
rows=3D7819999 width=3D16) (actual time=3D4414.476..4633.982 rows=3D1000000=
.00 loops=3D1)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Wo=
rkers Planned: 2<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0=
Workers Launched: 2<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0Buffers: shared hit=3D7883221 read=3D124111, temp read=3D20699 written=
=3D35385<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&gt; =
=C2=A0Sort =C2=A0(cost=3D7200203.05..7208348.88 rows=3D3258333 width=3D16) =
(actual time=3D4390.625..4411.896 rows=3D334567.00 loops=3D3)<br>=C2=A0 =C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Sort Key:=
 grid.b<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0Sort Method: <b>external merge =C2=A0Disk: 47304kB</b><br>=C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Bu=
ffers: shared hit=3D7883221 read=3D124111, temp read=3D20699 written=3D3538=
5<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0Worker 0: =C2=A0Sort Method: external merge =C2=A0Disk: 47304kB<br>=
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=
=A0Worker 1: =C2=A0Sort Method: external merge =C2=A0Disk: 46384kB<br>=C2=
=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0-&=
gt; =C2=A0<b>Parallel Index Scan</b> using grid_a_b_c_idx on grid =C2=A0(co=
st=3D0.57..6736351.43 rows=3D3258333 width=3D16) (actual time=3D46.925..379=
6.915 rows=3D2666666.67 loops=3D3)<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Index Cond: (=
(a =3D ANY (&#39;{2,3,5,8,13,21,34,55}&#39;::integer[])) AND (b &gt;=3D 0))=
<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =
=C2=A0 =C2=A0 =C2=A0 =C2=A0Index Searches: 7<br>=C2=A0 =C2=A0 =C2=A0 =C2=A0=
 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0Buffe=
rs: shared hit=3D7883208 read=3D124110<br>=C2=A0Planning Time: 0.385 ms<br>=
=C2=A0Execution Time: 4713.325 ms<br>=C2=A0```<br><br>=C2=A0</div><div><br>=
</div><div><br></div></div><div dir=3D"ltr"><br></div><br><div class=3D"gma=
il_quote"><div dir=3D"ltr" class=3D"gmail_attr">On Thu, Feb 5, 2026 at 6:59=
=E2=80=AFAM Alexandre Felipe &lt;<a href=3D"mailto:o.alexandre.felipe@gmail=
.com" target=3D"_blank">o.alexandre.felipe@gmail.com</a>&gt; wrote:<br></di=
v><blockquote class=3D"gmail_quote" style=3D"margin:0px 0px 0px 0.8ex;borde=
r-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir=3D"ltr">Thank =
you for looking into this.<div><br></div><div>Now we can execute a, still n=
arrow, family queries!</div><div><br></div><div>Maybe it helps to see this =
as a=C2=A0<u>social network=C2=A0feeds</u>. Imagine a social network, you h=
ave a few friends, or follow a few people, and you want to see their update=
s ordered by date. For each user we have a different combination of users t=
hat we have to display. But maybe, even having hundreds of users we will on=
ly show the first 10.</div><div><br></div><div>There is a low hanging fruit=
 on the skip scan, if we need N rows, and one group already has M rows we c=
ould stop there.</div><div>If Nx is the number of friends, and M is the num=
ber of posts to show.</div><div>This runs with complexity (Nx * M) rows, fo=
llowed by an (Nx * M) sort, instead of (Nx * N) followed by an (Nx * N) sor=
t.</div><div>Where M =3D 10 and N is 1000 this is a significant improvement=
.</div><div>But if M ~ N, the merge scan=C2=A0that runs with M=C2=A0+ Nx ro=
w accesses, (M=C2=A0+ Nx) heap operations.</div><div>If everything is on th=
e same page the skip scan would win.</div><div><br></div><div>The cost esti=
mation is probably far off.</div><div>I am also not considering the filters=
=C2=A0applied after this=C2=A0operator,=C2=A0and I don&#39;t know if the pl=
anner infrastructure is able to adjust it by itself.</div><div>This is wher=
e I would like reviewer&#39;s feedback. I think that the planner costs are =
something to be determined experimentally.</div><div><br></div><div>Next I =
will make it slightly more general handling<br>* More index columns: Index =
(a, b, s...) could support WHERE a IN (...) ORDER BY b LIMIT N (ignoring s.=
..)<br>* Multi-column prefix: WHERE (a, b) IN (...) ORDER BY c<br>* Non-lea=
ding prefix: WHERE b IN (...) AND a =3D const ORDER BY c on index (a, b, c)=
</div><div><br></div><div>---</div><div>Kind Regards,</div><div>Alexandre</=
div></div><br><div class=3D"gmail_quote"><div dir=3D"ltr" class=3D"gmail_at=
tr">On Wed, Feb 4, 2026 at 7:13=E2=80=AFAM Micha=C5=82 K=C5=82eczek &lt;<a =
href=3D"mailto:michal@kleczek.org" target=3D"_blank">michal@kleczek.org</a>=
&gt; wrote:<br></div><blockquote class=3D"gmail_quote" style=3D"margin:0px =
0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div=
><br id=3D"m_1178963958729505245m_7370567820092274636m_4579418652561517672m=
_3586735336800096661lineBreakAtBeginningOfMessage"><div><br><blockquote typ=
e=3D"cite"><div>On 3 Feb 2026, at 22:42, Ants Aasma &lt;<a href=3D"mailto:a=
nts.aasma@cybertec.at" target=3D"_blank">ants.aasma@cybertec.at</a>&gt; wro=
te:</div><br><div><div>On Mon, 2 Feb 2026 at 01:54, Tomas Vondra &lt;<a hre=
f=3D"mailto:tomas@vondra.me" target=3D"_blank">tomas@vondra.me</a>&gt; wrot=
e:<br><blockquote type=3D"cite">I&#39;m also wondering how common is the ta=
rgeted query pattern? How common<br>it is to have an IN condition on the le=
ading column in an index, and<br>ORDER BY on the second one?<br></blockquot=
e><br>I have seen this pattern multiple times. My nickname for it is the<br=
>timeline view. Think of the social media timeline, showing posts from<br>a=
ll followed accounts in timestamp order, returned in reasonably sized<br>ba=
tches. The naive SQL query will have to scan all posts from all<br>followed=
 accounts and pass them through a top-N sort. When the total<br>number of p=
osts is much larger than the batch size this is much slower<br>than what is=
 proposed here (assuming I understand it correctly) -<br>effectively equiva=
lent to running N index scans through Merge Append.</div></div></blockquote=
><blockquote type=3D"cite"><div><div><br>My workarounds I have proposed use=
rs have been either to rewrite the<br>query as a UNION ALL of a set of sing=
le value prefix queries wrapped<br>in an order by limit. This gives the exa=
ct needed merge append plan<br>shape. But repeating the query N times can g=
et unwieldy when the<br>number of values grows, so the fallback is:<br><br>=
SELECT * FROM unnest(:friends) id, LATERAL (<br> =C2=A0=C2=A0=C2=A0SELECT *=
 FROM posts<br> =C2=A0=C2=A0=C2=A0WHERE user_id =3D id<br> =C2=A0=C2=A0=C2=
=A0ORDER BY tstamp DESC LIMIT 100)<br>ORDER BY tstamp DESC LIMIT 100;<br><b=
r>The downside of this formulation is that we still have to fetch a<br>batc=
h worth of items from scans where we otherwise would have only had<br>to lo=
ok at one index tuple.<br></div></div></blockquote><div><br></div><div>GIST=
 can be used to handle this kind of queries as it supports multiple sort or=
ders.</div><div>The only problem is that GIST does not support ORDER BY col=
umn.</div><div>One possible workaround is [1] but as described there it doe=
s not play well with partitioning.</div><div>I=E2=80=99ve started drafting =
support for ORDER BY column in GIST - see [2].</div><div>I think it would b=
e easier to implement and maintain than a new IAM (but I don=E2=80=99t have=
 enough knowledge and experience to implement it myself)</div><div><br></di=
v><div>[1]=C2=A0<a href=3D"https://www.postgresql.org/message-id/3FA1E0A9-8=
393-41F6-88BD-62EEEA1EC21F%40kleczek.org" target=3D"_blank">https://www.pos=
tgresql.org/message-id/3FA1E0A9-8393-41F6-88BD-62EEEA1EC21F%40kleczek.org</=
a></div><div>[2]=C2=A0<a href=3D"https://www.postgresql.org/message-id/B2AC=
13F9-6655-4E27-BFD3-068844E5DC91%40kleczek.org" target=3D"_blank">https://w=
ww.postgresql.org/message-id/B2AC13F9-6655-4E27-BFD3-068844E5DC91%40kleczek=
.org</a></div><br></div>=E2=80=94<div>Kind regards,<br><div>Michal</div></d=
iv></div></blockquote></div>
</blockquote></div>
</div>
</div>

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