An efficient method of matrix multiplication for heaps of pieces

Abstract

In this paper, we outline a method for carrying out efficient (max, +) matrix multiplication when using the heaps of pieces framework. We present an algorithm for multiplying an arbitrary m by r matrix X by a r by r heaps of pieces matrix M, making it possible to calculate the resulting matrix in worst case time complexity O(mr), rather than O(mr2) which is required when using the matrix multiplication definition. We also give an algorithm for multiplying M by an arbitrary r by n matrix X with worst case time complexity O(nr). Finally, we consider a variant of the standard heaps of pieces model, and present an improved matrix multiplication algorithm for this variant as well.