Communication efficient matrix multiplication on hypercubes

Abstract

In a recent paper Fox, Otto and Hey consider matrix algorithms for hypercubes. For hypercubes allowing pipelined broadcast of messages they present a communication efficient algorithm. We present in this paper a similar algorithm that uses only nearest neighbour communication. This algorithm will therefore by very communication efficient also on hypercubes not allowing pipelined broadcast. We introduce a new algorithm that reduces the asymptotic communication cost from 2(N 2/P 1 2 )β to 3(N 2/P 2 3 )β . This is achieved by regarding the hypercube as a set of subcubes and by using the cascade sum algorithm.