I have a slots
table like this :
Column | Type |
------------+-----------------------------+
id | integer
Here is one method for solving this problem. Create a flag that determines if a one record does not overlap with the previous one. This is the start of a group. Then take the cumulative sum of this flag and use that for grouping:
select user_id, min(begin_at) as begin_at, max(end_at) as end_at
from (select s.*, sum(startflag) over (partition by user_id order by begin_at) as grp
from (select s.*,
(case when lag(end_at) over (partition by user_id order by begin_at) >= begin_at
then 0 else 1
end) as startflag
from slots s
) s
) s
group by user_id, grp;
Here is a SQL Fiddle.