Title: On the maximum number of fault-free mutually independent Hamiltonian cycles in the faulty hypercube
Authors: Kung, Tzu-Liang
Lin, Cheng-Kuan
Hsu, Lih-Hsing
Department of Computer Science
Keywords: Interconnection network;Graph;Hypercube;Fault tolerance;Hamiltonian cycle
Issue Date: 1-Feb-2014
Abstract: Hsieh and Yu (2007) first claimed that an injured n-dimensional hypercube Q (n) contains (n-1-f)-mutually independent fault-free Hamiltonian cycles, where fa parts per thousand currency signn-2 denotes the total number of permanent edge-faults in Q (n) for na parts per thousand yen4, and edge-faults can occur everywhere at random. Later, Kueng et al. (2009a) presented a formal proof to validate Hsieh and Yu's argument. This paper aims to improve this mentioned result by showing that up to (n-f)-mutually independent fault-free Hamiltonian cycles can be embedded under the same condition. Let F denote the set of f faulty edges. If all faulty edges happen to be incident with an identical vertex s, i.e., the minimum degree of the survival graph Q (n) -F is equal to n-f, then Q (n) -F contains at most (n-f)-mutually independent Hamiltonian cycles starting from s. From such a point of view, the presented result is optimal. Thus, not only does our improvement increase the number of mutually independent fault-free Hamiltonian cycles by one, but also the optimality can be achieved.
URI: http://dx.doi.org/10.1007/s10878-012-9528-1
ISSN: 1382-6905
DOI: 10.1007/s10878-012-9528-1
Volume: 27
Issue: 2
Begin Page: 328
End Page: 344
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