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

The known fast sequential algorithms for multiplying two NxN 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^α
, multiplying two NxN matrices can be performed on a p-processor linear array with a reconfigurable pipelined bus system (LARPBS) in O(N
_m
/P+(N
²
/p
²
α/)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 1^2.3755
, multiplying two NxN 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 NxN matrices can be performed on an LARPBS with O(N
^α
) processors in O(log N) time. This compares favorably with the performance on a PRAM.