Embedding paths of variable lengths into hypercubes with conditional link-faults |
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| Authors: | Tz-Liang Kueng Cheng-Kuan Lin Tyne Liang Jimmy JM Tan Lih-Hsing Hsu |
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| Affiliation: | aDepartment of Computer Science and Information Engineering, Asia University, 500 Lioufeng Rd., Taichung, Taiwan 41354, ROC;bDepartment of Computer Science, National Chiao Tung University, 1001 University Rd., Hsinchu, Taiwan 30050, ROC;cDepartment of Computer Science and Information Engineering, Providence University, 200 Chung Chi Rd., Taichung, Taiwan 43301, ROC |
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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 Qn, in which every node is still incident to at least two fault-free links. Then we show that Qn-F has a path of any odd (resp. even) length in the range from the distance to 2n-1 (resp. 2n-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. |
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| Keywords: | Interconnection network Hypercube Fault tolerance Conditional fault Linear array Path embedding |
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