Fault-Tolerant Permutation Routing in Hypercubes

Abstract

This paper introduces a deterministic mechanism for fault-tolerant permutation routing on an n-cube with less than n processor and/or link faults, using O( n) steps and constant queue size. The basic approach is to modify an existing route of a given permutation to avoid the faulty processors and/or faulty links, yet only incurring a constant factor slowdown in communication by ensuring that, at each step of the routing, every message either stays where it is or is sent to a nonfaulty neighbor, each link has at most one message traversing it in each direction, and the routing uses constant queue size. The existing route used in this paper is Benes routes. However, our method can be applied to any routing method where, in each step, all messages use links across the same dimension. The same approach can also be applied to online routing based on Batcher′s bitonic sorting to avoid faults.