At 05:16 PM 1/20/2006, Steinar H. Gunderson wrote:
>On Fri, Jan 20, 2006 at 04:50:17PM -0500, Tom Lane wrote:
> > I wonder if there is a way to improve on that.
>Ooh, the farthest pair problem (in an N-dimensional vector space, though).
>I'm pretty sure problems like this has been studied quite extensively in the
>literature, although perhaps not with the same norm. It's known under both
>"farthest pair" and "diameter", and probably others. I'm fairly sure it
>should be solvable in at least O(n log n).
If the N-dimensional space is Euclidean (any <x, x+1> is the same
distance apart in dimension x), then finding the farthest pair can be
done in at least O(n).
If you do not want the actual distance and can create the proper data
structures, particularly if you can update them incrementally as you
generate pairs, it is often possible to solve this problem in O(lg n) or O(1).
I'll do some grinding.