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The Computer Journal 1996 39(1):14-19; doi:10.1093/comjnl/39.1.14
© 1996 by British Computer Society
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An Efficient Algorithm for Node-to-node Routing in Hypercubes with Faulty Clusters

Q.-P. Gu * and S. Peng *

Department of Computer Software, The University of Aizu, Aizu-Wakamatsu, Fukushima 965-80, Japan

In this paper, we study the node-to-node fault tolerant routing problem in n-dimensional hypercubes Hn based on the cluster fault tolerant model. For a graph G, a faulty cluster is a connected subgraph of G such that all its nodes are faulty. In cluster fault tolerant routing problems, how many faulty clusters and how large those clusters can be tolerated are studied. It was proved that for node-to-node routing, Hn can tolerate as many as n – 1 faulty clusters of diameter at most 1 with at most 2n – 3 faulty nodes in total. In this paper, we give an algorithm which, given at most n – 1 faulty clusters of diameter at most 1 with 2n – 3 faulty nodes in total and non-faulty node s and t in Hn, finds a fault-free path s->t of length at most n + 2 in O(n) optimal time. The upper bound on the length of the path is optimal when the distance between s and t is n – 2.

Received May 30, 1995. revised November 27, 1995.

* Department of Computer Software, The University of Aizu, Aizu-Wakamatsu, Fukushima 965-80, Japan E-mail: qian{at}u-aizu.ac.jp


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