An Optimal Parallel Algorithm for Computing a Near-Optimal Order of Matrix Multiplications

This paper considers the computation of matrix chain products of the form M1 M2 Mn?1. The order in which the matrices are multiplied aaects the number of operations. The best sequential algorithm for computing an optimal order of matrix multiplication runs in O(n log n) time while the best known parallel NC algorithm runs in O(log 2 n) time using n 6 = log 6 n processors. This paper presents the rst approximating optimal parallel algorithm for this problem and for the problem of nding a near-optimal triangulation of a convex polygon. The algorithm runs in O(log n) time using n= log n processors on a CREW PRAM, and in O(log log n) time using n= log log n processors on a weak CRCW PRAM. It produces an order of matrix multiplications and a partition of polygon which diier from the optimal ones at most 0.1547 times.