Postgres: The best way to optmize "greater than" query - postgresql

Question

what is the best way to optimize join query that join with the same table on the next id value at the sub group? For now I have something like this:
CREATE OR REPLACE FUNCTION select_next_id(bigint, bigint) RETURNS bigint AS $body$
DECLARE
_id bigint;
BEGIN
SELECT id INTO _id FROM table WHERE id_group = $2 AND id > $1 ORDER BY id ASC LIMIT 1;
RETURN _id;
END;
$body$ LANGUAGE plpgsql;
And the JOIN query:
SELECT * FROM table t1
JOIN table t2 ON t2.id = select_next_id(t1.id, t1.id_group)
The table have more than 2kk rows, and it takes very very long. Is there a better way to do this quick? Also I have UNIQUE INDEX on column id. Not very helpfull I guess.
Some sample data:
id | id_group
=============
1 | 1
2 | 1
3 | 1
4 | 2
5 | 2
6 | 2
20 | 4
25 | 4
37 | 4
40 | 1
55 | 2
And I want to recieve something like this:
id | id_next
1 | 2
2 | 3
3 | null
4 | 5
5 | 6
6 | 55
and so on.

Answer 1

For the query in the function, you need an index on (id_group, id), not just (id).
Next, you don't need the overhead of plpgsql in the function itself, and you can give a few hints to the planner by making it as stable and having a small cost:
CREATE OR REPLACE FUNCTION select_next_id(bigint, bigint) RETURNS bigint AS $body$
SELECT id FROM table WHERE id_group = $2 AND id > $1 ORDER BY id ASC LIMIT 1;
$body$ LANGUAGE sql STABLE COST 10;
In the final query, depending on what you're actually trying to do, you might be able to get rid of the join and the function call by using lead() as highlighted by the horse:
http://www.postgresql.org/docs/current/static/tutorial-window.html

Answer 2

I'm not entirely sure, but I think you want something like this:
select id,
lead(id) over (partition by id_group order by id) as id_next
from the_table
order by id, id_next;