Universal schemes for parallel communication

Abstract

In this paper we isolate a combinatorial problem that, we believe, lies at the heart of this question and provide some encouragingly positive solutions to it. We show that there exists an N-processor realistic computer that can simulate arbitrary idealistic N-processor parallel computations with only a factor of O(log N) loss of runtime efficiency. The main innovation is an O(log N) time randomized routing algorithm. Previous approaches were based on sorting or permutation networks, and implied loss factors of order at least (log N)2.