Communication-efficient Parallel Graph Algorithms

Abstract

Communication bandwidth is a resource ignored by most parallel random-access machine (PRAM) models. This paper shows that many graph problems can be solved in parallel, not only with polylogarithmic performance, but with efficient communication at each step of the computation. We measure the communication requirements of an algorithm in a model called the distributed random-access machine (DRAM), in whcih communication cost is measured in terms of the congestion of memory access across cuts of an underlying network. The algorithms are based on a communication-efficient variant of the tree contraction technique due to Miller and Reif.