Fast execution of irregularly structured programs with low communication frequency on the hypercube

Abstract

In this paper we study the problem of efficiently executing a parallel program composed of N tasks on a 0(N)-node hypercube assuming that (a) communications between tasks are irregular i.e. any pair of tasks may want to communicate at any step of the program and (b) communications between any two tasks occur with a low frequency, i.e. frequency formula Presented. Our probabilistic technique emulates such programs with slowdown 0(log log N) with high probability. The problem can be also seen as the problem of emulating a CRCW PRAM program on a distributed memory parallel machine whose interconnection network is the hypercube and our result can be equivalently stated in this model. As a part of the emulation technique, we develop a Distributed Recombination Algorithm that has independent interest being an efficient way of clustering homogenous information on a hypercube.