EVALUATION OF MATRIX CHAIN PRODUCTS ON PARALLEL SYSTEMSy

The problem of nding an optimal product sequence for sequential multiplication of matrices (the matrix chain ordering problem, MCOP) is well-known and has been studied for a long time. In this paper, we consider the problem of nding an optimal product schedule for evaluating a chain of matrix products on a parallel computer (the matrix chain scheduling problem, MCSP). The diierence between MCSP and MCOP is that MCOP considers a product sequence for single processor systems and MCSP considers a sequence of concurrent matrix products for parallel systems. The approach of parallelizing each matrix product after nding an optimal product sequence for single processor systems does not always guarantee a minimal evaluation time since each parallelized matrix product may use processors ineeciently. We introduce a processor scheduling algorithm for MCSP which attempts to minimize the evaluation time of a chain of matrix products on a parallel computer, even at the expense of a slight increase in the total number of operations. Experiments on Fujitsu AP1000 multicomputer show that the proposed algorithm decreases the time required to evaluate a chain of matrix products in actual parallel systems.