Flattening intersecting timespans

Question

I have lots of data with start and stop times for a given ID and I need to flatten all intersecting and adjacent timespans into one combined timespan. The sample data posted below is all for the same ID so I didn't list it.

To make things a bit clearer, take a look at the sample data for 03.06.2009:

The following timespans are overlapping or contiunous and need to merge into one timespan

• 05:54:48 - 10:00:13
• 09:26:45 - 09:59:40

The resulting timespan would be from 05:54:48 to 10:00:13. Since there's a gap between 10:00:13 and 10:12:50 we also have the following timespans:

• 10:12:50 - 10:27:25
• 10:13:12 - 11:14:56
• 10:27:25 - 10:27:31
• 10:27:39 - 13:53:38
• 11:14:56 - 11:15:03
• 11:15:30 - 14:02:14
• 13:53:38 - 13:53:43
• 14:02:14 - 14:02:31

which result in one merged timespan from 10:12:50 to 14:02:31, since they're overlapping or adjacent.

Below you will find the sample data and the flattened data as I would need it. The duration column is just informative.

Any solution - be it SQL or not - is appreciated.

---

EDIT: Since there are lots of different and interesting solutions I'm refining my original question by adding constraints to see the "best" (if there is one) solution bubble up:

• I'm getting the data via ODBC from another system. There's no way to change the table layout for me or adding indexes
• The data is indexed only by the date column (the time part isn't)
• There are about 2.5k rows for every day
• The estimated usage pattern of the data is roughly as follows:
  • Most of the time (lets say 90%) the user will query just one or two days (2.5k - 5k rows)
  • Sometimes (9%) the range will be up to a month (~75k rows)
  • Rarely (1%) the range will be up to a year (~900k rows)
• The query should be fast for the typical case and not "last forever" for the rare case.
• Querying a year worth of data takes about 5 minutes (plain select without joins)

Within these constraints, what would be the best solution? I'm afraid that most of the solutions will be horribly slow since they join on the combination of date and time, which is not an index field in my case.

Would you do all the merging on the client or the server side? Would you first create an optimized temp table and use one of the proposed solutions with that table? I didn't have the time to test the solutions until now but I will keep you informed what works best for me.

---

Sample data:

Date       | Start    | Stop
-----------+----------+---------
02.06.2009 | 05:55:28 | 09:58:27
02.06.2009 | 10:15:19 | 13:58:24
02.06.2009 | 13:58:24 | 13:58:43
03.06.2009 | 05:54:48 | 10:00:13
03.06.2009 | 09:26:45 | 09:59:40
03.06.2009 | 10:12:50 | 10:27:25
03.06.2009 | 10:13:12 | 11:14:56
03.06.2009 | 10:27:25 | 10:27:31
03.06.2009 | 10:27:39 | 13:53:38
03.06.2009 | 11:14:56 | 11:15:03
03.06.2009 | 11:15:30 | 14:02:14
03.06.2009 | 13:53:38 | 13:53:43
03.06.2009 | 14:02:14 | 14:02:31
04.06.2009 | 05:48:27 | 09:58:59
04.06.2009 | 06:00:00 | 09:59:07
04.06.2009 | 10:15:52 | 13:54:52
04.06.2009 | 10:16:01 | 13:24:20
04.06.2009 | 13:24:20 | 13:24:24
04.06.2009 | 13:24:32 | 14:00:39
04.06.2009 | 13:54:52 | 13:54:58
04.06.2009 | 14:00:39 | 14:00:49
05.06.2009 | 05:53:58 | 09:59:12
05.06.2009 | 10:16:05 | 13:59:08
05.06.2009 | 13:59:08 | 13:59:16
06.06.2009 | 06:04:00 | 10:00:00
06.06.2009 | 10:16:54 | 10:18:40
06.06.2009 | 10:18:40 | 10:18:45
06.06.2009 | 10:23:00 | 13:57:00
06.06.2009 | 10:23:48 | 13:57:54
06.06.2009 | 13:57:21 | 13:57:38
06.06.2009 | 13:57:54 | 13:57:58
07.06.2009 | 21:59:30 | 01:58:49
07.06.2009 | 22:12:16 | 01:58:39
07.06.2009 | 22:12:25 | 01:58:28
08.06.2009 | 02:10:33 | 05:56:11
08.06.2009 | 02:10:43 | 05:56:23
08.06.2009 | 02:10:49 | 05:55:59
08.06.2009 | 05:55:59 | 05:56:01
08.06.2009 | 05:56:11 | 05:56:14
08.06.2009 | 05:56:23 | 05:56:27

Flattened result:

Date       | Start    | Stop     | Duration
-----------+----------+----------+---------
02.06.2009 | 05:55:28 | 09:58:27 | 04:02:59
02.06.2009 | 10:15:19 | 13:58:43 | 03:43:24
03.06.2009 | 05:54:48 | 10:00:13 | 04:05:25
03.06.2009 | 10:12:50 | 14:02:31 | 03:49:41
04.06.2009 | 05:48:27 | 09:59:07 | 04:10:40
04.06.2009 | 10:15:52 | 14:00:49 | 03:44:58
05.06.2009 | 05:53:58 | 09:59:12 | 04:05:14
05.06.2009 | 10:16:05 | 13:59:16 | 03:43:11
06.06.2009 | 06:04:00 | 10:00:00 | 03:56:00
06.06.2009 | 10:16:54 | 10:18:45 | 00:01:51
06.06.2009 | 10:23:00 | 13:57:58 | 03:34:58
07.06.2009 | 21:59:30 | 01:58:49 | 03:59:19
08.06.2009 | 02:10:33 | 05:56:27 | 03:45:54

Answer 1

Here is a SQL only solution. I used DATETIME for the columns. Storing the time separate is a mistake in my opinion, as you will have problems when the times go past midnight. You can adjust this to handle that situation though if you need to. The solution also assumes that the start and end times are NOT NULL. Again, you can adjust as needed if that's not the case.

The general gist of the solution is to get all of the start times that don't overlap with any other spans, get all of the end times that don't overlap with any spans, then match the two together.

The results match your expected results except in one case, which checking by hand looks like you have a mistake in your expected output. On the 6th there should be a span that ends at 2009-06-06 10:18:45.000.

SELECT
     ST.start_time,
     ET.end_time
FROM
(
     SELECT
          T1.start_time
     FROM
          dbo.Test_Time_Spans T1
     LEFT OUTER JOIN dbo.Test_Time_Spans T2 ON
          T2.start_time < T1.start_time AND
          T2.end_time >= T1.start_time
     WHERE
          T2.start_time IS NULL
) AS ST
INNER JOIN
(
     SELECT
          T3.end_time
     FROM
          dbo.Test_Time_Spans T3
     LEFT OUTER JOIN dbo.Test_Time_Spans T4 ON
          T4.end_time > T3.end_time AND
          T4.start_time <= T3.end_time
     WHERE
          T4.start_time IS NULL
) AS ET ON
     ET.end_time > ST.start_time
LEFT OUTER JOIN
(
     SELECT
          T5.end_time
     FROM
          dbo.Test_Time_Spans T5
     LEFT OUTER JOIN dbo.Test_Time_Spans T6 ON
          T6.end_time > T5.end_time AND
          T6.start_time <= T5.end_time
     WHERE
          T6.start_time IS NULL
) AS ET2 ON
     ET2.end_time > ST.start_time AND
     ET2.end_time < ET.end_time
WHERE
     ET2.end_time IS NULL