postgres select aggregate timespans

I have a table with the following structure:

timstamp-start, timestamp-stop
1,5
6,10
25,30
31,35
...

I am only interested in continuous timespans e.g. the break between a timestamp-end and the following timestamp-start is less than 3.

How could I get the aggregated covered timespans as a result:

timestamp-start,timestamp-stop
1,10
25,35

The reason I am considering this is because a user may request a time span that would need to return several thousand rows. However, most records are continuous and using above method could potentially reduce many thousand of rows down to just a dozen. Or is the added computation not worth the savings in bandwidth and latency?

For example: if the values are 1,5 and 7,10, I don’t want 2 rows because 5 and 7 are less than three apart so I want them to be combined into one row (1,10)

All credit for this answer goes to Dudu Markovitz. I think this is a bit different, but I’m using his method and you should read his explanation.

Test data:

CREATE TABLE foo(a,b) AS
SELECT *
FROM ( VALUES (1,5), (6,10), (25,30), (31,35) ) AS x;

Here is the query I created,

SELECT min(a), max(b) FROM (
  SELECT a,
  b,
  count(reset) OVER (ORDER BY a,b) AS grp
FROM (
    SELECT
      a,
      b,
      CASE WHEN a-(lag(b) OVER ()) > 3 THEN 1 END AS reset
    FROM foo
    ORDER BY a,b
  ) AS f1 
) as f2
GROUP BY grp
ORDER BY grp;

I’ll break it down the same way… Here we establish resets to mark new ranges.

SELECT
  a,
  b,
  CASE WHEN a-(lag(b) OVER ()) > 3 THEN 1 END AS reset
FROM foo
ORDER BY a,b;

gives us this

 a  | b  | reset 
----+----+-------
  1 |  5 |      
  6 | 10 |      
 25 | 30 |     1
 31 | 35 |      

Then we count(reset) OVER (ORDER BY a,b) to get

 a  | b  | grp 
----+----+-----
  1 |  5 |   0
  6 | 10 |   0
 25 | 30 |   1
 31 | 35 |   1

Then we wrap that whole thing in a sub-select GROUP BY grp and pick min(a) and max(b) which does what you want.