overlapping hyperrectangles

From: Craig Schmidt (cschmidt_at_rcn.com)
Date: 01/23/04 

Date: Thu, 22 Jan 2004 23:06:50 -0500

Hi Everyone,

Say you have a set of n hyperrectangles that all contain a known point. I
want to find the pair of hyperrectangles that overlap each other the most in
terms of volume. I'll settle for an approximate or probabilistic solutions,
giving me a pair that overlaps signficantly.

Clearly you can compute the overlap of each pair of hyperrectangles, and
pick the best, which takes O(n^2) time. Is it possible to do it faster?

Thanks for any suggestions or leads.

Craig Schmidt