An approach to conditional diagnosability analysis under the PMC model and its application to torus networks

Kim, Hee-Chul; Lim, Hyeong-Seok; Park, Jung-Heum

doi:10.1016/j.tcs.2014.07.006

Cited by 9 publications

(2 citation statements)

References 27 publications

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“…One crucial parameter to evaluate the fault tolerability of a network is its connectivity. The connectivity of a graph G, denoted by κ(G), is the minimum cardinality of a node set F ⊆ V (G), such that F's deletion disconnects G. As variants of the classic node-connectivity, several kinds of conditional connectivity were proposed and studied [2], [3], [5], [6], [8], [9], [12]- [16], [18], [23], [25], [26]. Notably among them, Fàbrega and Fiol [4] introduced the g-extra connectivity.…”

Section: A Connectivity Of Interconnection Networkmentioning

confidence: 99%

Structure Connectivity and Substructure Connectivity of $k$ -Ary $n$ -Cube Networks

Zhang

Wang

2019

IEEE Access

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We present new results on the fault tolerability of k-ary n-cube (denoted Q k n ) networks. Q k n is a topological model for interconnection networks that has been extensively studied since proposed, and this paper is concerned with the structure/substructure connectivity of Q k n networks, for paths and cycles, two basic yet important network structures. Let G be a connected graph and T a connected subgraph of G.The T -structure connectivity κ(G; T ) of G is the cardinality of a minimum set of subgraphs in G, such that each subgraph is isomorphic to T , and the set's removal disconnects G. The T -substructure connectivity κ s (G; T ) of G is the cardinality of a minimum set of subgraphs in G, such that each subgraph is isomorphic to a connected subgraph of T , and the set's removal disconnects G. In this paper, we study κ(Q k n ; T ) and κ s (Q k n ; T ) for T = P i , a path on i nodes (resp. T = C i , a cycle on i nodes). Lv et al. determined κ(Q k n ; T ) and κ s (Q k n ; T ) for T ∈ {P 1 , P 2 , P 3 }. Our results generalize the preceding results by determining κ(Q k n ; P i ) and κ s (Q k n ; P i ). In addition, we have also established κ(Q k n ; C i ) and κ s (Q k n ; C i ).

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Section: A Connectivity Of Interconnection Networkmentioning

confidence: 99%

Structure Connectivity and Substructure Connectivity of $k$ -Ary $n$ -Cube Networks

Zhang

Wang

2019

IEEE Access

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“…Torus networks are a class of regular networks [ 20 ]. Due to the superiority in unicast routing [ 21 – 26 ], multicast routing [ 27 ] and fault tolerance [ 28 ], torus networks frequently serve as the underlying interconnection network of a multicomputer system. To our knowledge, there is no report in literature on the OLR problem for torus networks.…”

Section: Introductionmentioning

confidence: 99%

Reducing the Spectral Radius of a Torus Network by Link Removal

Yang

et al. 2016

PLoS ONE

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The optimal link removal (OLR) problem aims at removing a given number of links of a network so that the spectral radius of the residue network obtained by removing the links from the network attains the minimum. Torus networks are a class of regular networks that have witnessed widespread applications. This paper addresses three subproblems of the OLR problem for torus networks, where two or three or four edges are removed. For either of the three subproblems, a link-removing scheme is described. Exhaustive searches show that, for small-sized tori, each of the proposed schemes produces an optimal solution to the corresponding subproblem. Monte-Carlo simulations demonstrate that, for medium-sized tori, each of the three schemes produces a solution to the corresponding subproblem, which is optimal when compared to a large set of randomly produced link-removing schemes. Consequently, it is speculated that each of the three schemes produces an optimal solution to the corresponding subproblem for all torus networks. The set of links produced by each of our schemes is evenly distributed over a network, which may be a common feature of an optimal solution to the OLR problem for regular networks.

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Fault tolerance assessment for hamming graphs based on r-restricted R-structure(substructure) fault pattern

Yang,

Zhang,

Meng

2025

Applied Mathematics and Computation

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An approach to conditional diagnosability analysis under the PMC model and its application to torus networks

Cited by 9 publications

References 27 publications

Structure Connectivity and Substructure Connectivity of $k$ -Ary $n$ -Cube Networks

Structure Connectivity and Substructure Connectivity of $k$ -Ary $n$ -Cube Networks

Reducing the Spectral Radius of a Torus Network by Link Removal

Fault tolerance assessment for hamming graphs based on r-restricted R-structure(substructure) fault pattern

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