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An <span class="MathJax_Preview" style="">O({\log}_2(N))</span><script type="math/tex" id="MathJax-Element-1">O({\log}_2(N))</script> Algorithm for Reliability Evaluation of <span class="MathJax_Preview" style="">h</span><script type="math/tex" id="MathJax-Element-2">h</script>-Extra Edge-Connectivity of Folded Hypercubes | IEEE Journals & Magazine | IEEE Xplore

An O({\log}_2(N)) Algorithm for Reliability Evaluation of h-Extra Edge-Connectivity of Folded Hypercubes


Abstract:

Reliability analysis of an interconnection network is of great significance to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of a gi...Show More

Abstract:

Reliability analysis of an interconnection network is of great significance to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of a given interconnected network G with N processors, denoted by λh(G), is the minimum cardinality of set of faulty links, such that whose removal will disconnect the network with all its resulting components having at least h processors for h ≤ N/2. It gives a more refined quantitative analysis of indicators of the robustness of a multiprocessor system in the presence of failing links. The n-dimensional folded hypercube FQn, as one of potential interconnected networks, is a well-known variation of the hypercube structure with N = 2n processors. In this paper, the h-extra edge-connectivity of the network FQn, λh(FQn), is first investigated for each well-defined positive integer h ≤ N/2. We divide the interval 1 ≤ h ≤ N/2 into some subintervals and obtain some properties of λh(FQn) in these subintervals. Then, we deduce a recursive relation of λh(F Qn). Based on this recursion, an efficient O(log2 (N)) algorithm is designed to totally determine the exact values and λh-optimality of λh(FQn) for each h ≤ N/2.
Published in: IEEE Transactions on Reliability ( Volume: 67, Issue: 1, March 2018)
Page(s): 297 - 307
Date of Publication: 09 January 2018

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