It is unclear to me how you got from your input data to your expected output. If you are "trying to count() overlapping entries" then it would seem to me that you would only have only one value for the count. Either a range overlaps or it does not.
Oh, sorry, the count was in wrong order.
Let me explain,
insert into event(name, start_time, end_time) values('a', '2015-12-20', NULL) , ('a', '2015-12-20', '2015-12-31') , ('a', '2015-12-25', '2016-01-01') , ('b', '2015-11-20', '2015-11-24') , ('c', '2016-02-01', '2016-02-03') , ('c', '2016-02-01', '2016-02-04')
, ('c', '2016-02-01', NULL)
;
All 'a', 'b' and 'c' have points in common, with count a=3, b=1, c=3.
Note that the 'name'-column here is just to explain what I'm after and that I have no such column.
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Andreas Joseph Krogh
CTO / Partner - Visena AS
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