Parallel matrix multiplication on a linear array with a reconfigurable pipelined bus system

The known fast sequential algorithms for multiplying two N×N matrices (over an arbitrary ring) have time complexity O(N^α ), where 2<α<3. The current best value of α is less than 2.3755. We show that for all 1⩽p⩽N^α, multiplying two N×N matrices can be performed on a p-processor linear array with a reconfigurable pipelined bus system (LARPBS) in O(N ^α/p+(N²/p²α/)log p) time. This is currently the fastest parallelization of the best known sequential matrix multiplication algorithm on a distributed memory parallel system