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Issue No. 09 - September (1997 vol. 46)
ISSN: 0018-9340
pp: 1042-1049
<p><b>Abstract</b>—In this paper, we introduce a general fault tolerant routing problem, <it>cluster fault tolerant routing</it>, which is a natural extension of the well studied node fault tolerant routing problem. A cluster is a connected subgraph of a graph <it>G</it>, and a cluster is faulty if all nodes in it are faulty. In <it>cluster fault tolerant routing</it> (abbreviated as CFT routing), we are interested in the number of faulty clusters and the size of the clusters that an interconnection network can tolerate for certain routing problems. As a case study, we investigate the following <it>k</it>-pairwise CFT routing in <it>n</it>-dimensional hypercubes <it>H</it><sub><it>n</it></sub>: Given a set of faulty clusters and <it>k</it> distinct nonfaulty node pairs (<it>s</it><sub>1</sub>, <it>t</it><sub>1</sub>), ..., (<it>s</it><sub><it>k</it></sub>, <it>t</it><sub><it>k</it></sub>) in <it>H</it><sub><it>n</it></sub>, find <it>k</it> fault-free node-disjoint paths <it>s</it><sub><it>i</it></sub>→<it>t</it><sub><it>i</it></sub>, 1 ≤<it>i</it>≤<it>k</it>. We show that <it>H</it><sub><it>n</it></sub> can tolerate <it>n</it>− 2 faulty clusters of diameter one, plus one faulty node for the <it>k</it>-pairwise CFT routing with <it>k</it> = 1. For <it>n</it>≥ 4 and <tmath>$2 \le k \le \lceil n/2 \rceil,$</tmath> we prove that <it>H</it><sub><it>n</it></sub> can tolerate <it>n</it>− 2<it>k</it> + 1 faulty clusters of diameter one for the <it>k</it>-pairwise CFT routing. We also give an <it>O</it>(<it>kn</it> log <it>n</it>) time algorithm which finds the <it>k</it> paths for the mentioned problem. Our algorithm implies an <it>O</it>(<it>n</it><super>2</super> log <it>n</it>) time algorithm for the <it>k</it>-pairwise node-disjoint paths problem in <it>H</it><sub><it>n</it></sub>, which improves the previous result of <it>O</it>(<it>n</it><super>3</super> log <it>n</it>).</p>
Interconnection networks, algorithms, node-disjoint paths, node fault tolerant routing.
Shietung Peng, Qian-Ping Gu, "k-Pairwise Cluster Fault Tolerant Routing in Hypercubes", IEEE Transactions on Computers, vol. 46, no. , pp. 1042-1049, September 1997, doi:10.1109/12.620486
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