Embedding paths of variable lengths into hypercubes with conditional link-faults

Authors:
Tz-Liang Kueng;Cheng-Kuan Lin;Tyne Liang;Jimmy J. M. Tan;Lih-Hsing Hsu
Affiliations:
Department of Computer Science and Information Engineering, Asia University, 500 Lioufeng Rd., Taichung, Taiwan 41354, ROC;Department of Computer Science, National Chiao Tung University, 1001 University Rd., Hsinchu, Taiwan 30050, ROC;Department of Computer Science, National Chiao Tung University, 1001 University Rd., Hsinchu, Taiwan 30050, ROC;Department of Computer Science, National Chiao Tung University, 1001 University Rd., Hsinchu, Taiwan 30050, ROC;Department of Computer Science and Information Engineering, Providence University, 200 Chung Chi Rd., Taichung, Taiwan 43301, ROC
Venue:
Parallel Computing
Year:
2009

Citing 18
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Abstract

Faults in a network may take various forms such as hardware failures while a node or a link stops functioning, software errors, or even missing of transmitted packets. In this paper, we study the link-fault-tolerant capability of an n-dimensional hypercube (n-cube for short) with respect to path embedding of variable lengths in the range from the shortest to the longest. Let F be a set consisting of faulty links in a wounded n-cube Q"n, in which every node is still incident to at least two fault-free links. Then we show that Q"n-F has a path of any odd (resp. even) length in the range from the distance to 2^n-1 (resp. 2^n-2) between two arbitrary nodes even if |F|=2n-5. In order to tackle this problem, we also investigate the fault diameter of an n-cube with hybrid node and link faults.