An O(2(N)) Algorithm for Reliability Evaluation of h-Extra Edge-Connectivity of Folded Hypercubes

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 λ h (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 FQ n , as one of potential interconnected networks, is a well-known variation of the hypercube structure with N = 2 n processors. In this paper, the h-extra edge-connectivity of the network FQ n , λ h (FQ n ), 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 λ h (FQ n ) in these subintervals. Then, we deduce a recursive relation of λh(F Qn). Based on this recursion, an efficient O(log 2 (N)) algorithm is designed to totally determine the exact values and λ h -optimality of λ h (FQ n ) for each h ≤ N/2.