2013
DOI: 10.1016/j.ipl.2013.04.007
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Generalized measures of fault tolerance in exchanged hypercubes

Abstract: The exchanged hypercube EH(s, t), proposed by Loh et al. [The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866-874], is obtained by removing edges from a hypercube Q s+t+1 . This paper considers a kind of generalized measures κ (h) and λ (h) of fault tolerance in EH(s, t) with 1 s t and determines κ (h) (EH(s, t)) = λ (h) (EH(s, t)) = 2 h (s + 1 − h) for any h with 0 h s. The results show that at least 2 h (s + 1 − h) vertices (resp. 2 h (s + 1 − h) edges) of EH(s, t… Show more

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Cited by 69 publications
(15 citation statements)
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“…A good peer-to-peer (P2P) network should have lower diameter and lower degree, and hence, the exchanged hypercube can be used to serve as a logical topology in a P2P environment [17]. Some related works on exchanged hypercubes have been studied, such as domination number [18], fault-tolerance measurement [19], connectivity [20], super connectivity [21], wide and fault diameters [22], and optimal edge congestion [23]. To the best of our knowledge, however, the RWA problem for implementing exchanged hypercube communication patterns on ring-connected WDM optical networks has not been investigated.…”
Section: Copyright C 2017 the Institute Of Electronics Information Amentioning
confidence: 99%
“…A good peer-to-peer (P2P) network should have lower diameter and lower degree, and hence, the exchanged hypercube can be used to serve as a logical topology in a P2P environment [17]. Some related works on exchanged hypercubes have been studied, such as domination number [18], fault-tolerance measurement [19], connectivity [20], super connectivity [21], wide and fault diameters [22], and optimal edge congestion [23]. To the best of our knowledge, however, the RWA problem for implementing exchanged hypercube communication patterns on ring-connected WDM optical networks has not been investigated.…”
Section: Copyright C 2017 the Institute Of Electronics Information Amentioning
confidence: 99%
“…The cardinality of the minimum g-good-neighbor conditional cut is said to be the R g -connectivity of G; denoted by k g ðGÞ: As a more refined index than the traditional connectivity, the R g -connectivity can be used to measure of conditional fault tolerance of networks. There are many results concerning the R g -connectivity for particular classes of interconnection networks and small g's, such as [9], [12], [25], [26], [35], [41], [42], [45]. But, with regard to general integer g; little information has been found.…”
Section: K K K-ary N N N-cubementioning
confidence: 99%
“…It is known that there exists no polynomial time algorithm to compute the g-connectivity and h-connectivity of a general graph [2,6]. The h-connectivity [4,14,23,24,26,35] and g-connectivity [3,10,15,28,34,36] of some famous networks are investigated in the literature.…”
Section: Introductionmentioning
confidence: 99%