Parallel Matrix Multiplication on a Linear Array with a Reconngurable Pipelined Bus System Parallel Matrix Multiplication on a Linear Array with a Reconngurable Pipelined Bus System

The known fast sequential algorithms for multiplying two N N matrices (over an arbitrary ring) have time complexity O(N), where 2 < < 3. The current best value of is less than 2.3755. We show that for all 1 p N , multiplying two N N matrices can be performed on a p-processor linear array with a reconngurable pipelined bus system (LARPBS) in O N p + N 2 p 2== log p time. This is currently the fastest parallelization of the best known sequential matrix multiplication algorithm on a distributed memory parallel system. In particular, for all 1 p N 2:3755 , multiplying two N N matrices can be performed on a p-processor LARPBS in O N 2:3755 p + N 2 p 0:8419 log p time, and linear speedup can be achieved for p as large as O(N 2:3755 =(log N) 6:3262). Furthermore, multiplying two NN matrices can be performed on an LARPBS with O(N) processors in O(log N) time. This compares favorably with the performance on a PRAM.