k-pairwise cluster fault tolerant routing in hypercubes

Abstract

In this paper, we introduce a general fault-tolerant routing problem, CFT routing, which is a natural extension of the well studied node fault tolerant routing problem, and give some CFT properties about k-pairwise CFT routing in n-dimensional hypercubes H _n. We give an O(n ² log n) time algorithm for k-pairwise CFT routing in H _n. Our algorithm imply an O(n ² log n) algorithm for k-pairwise node disjoint path problem in H _n. The algorithm for k-pairwise node disjoint path problem in H _n significantly improves the previous results of time complexity O(n ³ log n). As an extension of the fault diameter, we define cluster fault diameter for interconnection networks and prove the cluster fault diameter of H _n is n+2 when the diameters of the fault clusters are at most 1. We also show an O(n) time algorithm which finds a path of length at most n+3 for node-to-node CFT routing (k-pairwise CFT routing with k = 1) in H _n.

This research was partially supported by the Founding of Group Research Projects at Aizu University.