Join by date range unacceptably slow (2 replies)

Did I construct an inefficient UPDATE statement?

I am trying to update the column match_count, initially set to NULL, in table B with the count of matching records in table A. A record in table A is a match to a record in table B if the start and end times in table A overlap the start and end times in table B. This is the query statement I used:

UPDATE B
SET B.match_count = (
SELECT COUNT(*)
FROM A
WHERE A.start_time BETWEEN B.start_time and B.end_time
or B.start_time between A.start_time and A.end_time
)
WHERE B.match_count IS NULL
ORDER BY B.id
LIMIT 15000;

I had to set the 15000 limit and add the NULL test, so that it would run in under 10 minutes; otherwise the update would fail with a timeout. I created an index on each of A.start_time, A.end_time, B.start_time, B.end_time, A.start_time + A.end_time, B.start_time + B.end_time, B.match_count, but still the update takes what I thought to be an exceptionally long time.
Table A has 76,388 records and table B has 195,191 records.
Any insight is greatly appreciated.