New upper bounds in Klee's measure problem

Authors:
M. H. Overmars;Chee-Keng Yap
Affiliations:
Dept. of Comput. Sci., Utrecht Univ., Netherlands;-
Venue:
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Year:
1988

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Abstract

New upper bounds are given for the measure problem of V. Klee (1977) that significantly improve the previous bounds for dimensions greater than 2. An O(n/sup d/2/ log n, n) time-space upper bound to compute the measure of a set of n boxes in Euclidean d-space is obtained. The solution requires several novel ideas including application of the inclusion/exclusion principle, the concept of trellises, streaming, and a partition of d-space.