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Fault-tolerant cycle embedding in the hypercube

✍ Scribed by Jung-Sheng Fu

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
205 KB
Volume
29
Category
Article
ISSN
0167-8191

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✦ Synopsis

Almost all the previous fault-tolerant cycle embedding research could not tolerate the faulty nodes more than the degree of the network. In this paper, we have broken this limitation: a recursive method of embedding a longest cycle into an n-dimensional hypercube (n-cube), which can tolerate atmost 2n Γ€ 4 faulty nodes, is proposed. The best result thus far is to tolerate only atmost n Γ€ 1 faulty nodes, which is less than the degree of the n-cube.

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Let f e (respectively, f v ) denote the number of faulty edges (respectively, vertices) of an n-dimensional hypercube Q n . In this paper, we prove that every fault-free edge of Q n for n β‰₯ 3 lies on a fault-free cycle of every even length from 4 to 2 n -2 f v inclusive if f e + f v ≀ n -2. Furtherm

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## Abstract A hierarchical cubic network was proposed as an alternative to the hypercube. By HCN(__n__), we denote the hierarchical cubic network that contains 2^__n__^ __n__‐dimensional hypercubes. In this paper, using Gray codes, we construct fault‐free Hamiltonian cycles in an HCN(__n__) with __