MPI-I-92-123

Given a three dimensional orthogonal polyhedron P, we present a simple and efficient algorithm for finding the three dimensional orthogonal hyper-rectangle R of maximum volume, such that R is completely contained in P. Our algorithm finds out the three dimensional hyper-rectangle of maximum volume by using space sweep technique and enumerating all possible such rectangles. The presented algorithm runs in O(($n^2$+K)logn) time using O(n) space, where n is the number of vertices of the given polyhedron P and K is the number of reported three dimensional orthogonal hyper-rectangles for a problem instance, which is O($n^3$) in the worst case.