New upper bounds in Klee's measure problem

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.<
>