Minimum deadlock-free message routing restrictions in binary hypercubes

Abstract

This article presents a minimum set of deadlock-free routing restrictions (referred to as the Restriction) for binary hypercube networks and a new deadlock-free multiple-path fixed routing algorithm which provides a total of k + 1 arc-disjoint paths between two nodes of distance k. It is known that deadlock can be prevented by routing restriction in some highly regular networks. However, since routing restrictions imply a limited utilization of the existing paths, there should be as few restrictions as possible. The Restriction presented here is a relaxed version of the restrictions implied by the normal fixed routing algorithm. Proofs are presented to show that any routing that complies with the Restriction is deadlock-free and that the Restriction is minimal in that any relaxation to the Restriction will cause deadlock. The multiple-path fixed routing algorithm presented in this article fully utilizes the arc-disjoint paths allowed by the Restriction. The algorithm can be obtained by a small modification to the normal fixed routing algorithm. Results from a simulation of the hypercube network using the new routing algorithm is presented, which shows that the new algorithm improves the communication capacity of the hypercube.