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Klee's Measure Problem Made Easy
2013
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
We present a new algorithm for a classic problem in computational geometry, Klee's measure problem: given a set of n axis-parallel boxes in d-dimensional space, compute the volume of the union of the boxes. The algorithm runs in O(n d/2 ) time for any constant d ≥ 3. Although it improves the previous best algorithm by "just" an iterated logarithmic factor, the real surprise lies in the simplicity of the new algorithm. We also show that it is theoretically possible to beat the O(n d/2 ) time
doi:10.1109/focs.2013.51
dblp:conf/focs/Chan13
fatcat:c5st2mw2mbcglpxhoatw2aymzu