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

✍ Scribed by Tz-Liang Kueng; Cheng-Kuan Lin; Tyne Liang; Jimmy J.M. Tan; Lih-Hsing Hsu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 432 KB
• Volume: 35
• Category: Article
• ISSN: 0167-8191
• DOI: 10.1016/j.parco.2009.06.002

✦ Synopsis

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 À F has a path of any odd (resp. even) length in the range from the distance to 2 n À 1 (resp. 2 n À 2) between two arbitrary nodes even if jFj ¼ 2n À 5. In order to tackle this problem, we also investigate the fault diameter of an n-cube with hybrid node and link faults.