3D Rectangulations and Geometric Matrix Multiplication
The problem of partitioning an orthogonal polyhedron P into a minimum number of 3D rectangles is known to be NP-hard. In this paper, we first develop a 4-approximation algorithm for the special case of the problem in which P is a 3D histogram. It runs in O(mlogm) time, where m is the number of corners in P. We then apply it to exactly compute the arithmetic matrix product of two n×n matrices A and