k-pairwise cluster fault tolerant routing in hypercubes
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 Hn. We give an O(n2 log n) time algorithm for k-pairwise CFT routing in Hn. Our algorithm imply an O(n2 log n) algorithm for k-pairwise node disjoint path problem in Hn. The algorithm for k-pairwise node disjoint path problem in Hn significantly improves the previous results of time complexity O(n3 log n). As an extension of the fault diameter, we define cluster fault diameter for interconnection networks and prove the cluster fault diameter of Hn 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 Hn.
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