TOPOLOGICAL PROPERTIES OF THE (n,k)-STAR GRAPH

Chiang, Wei-Kuo; Chen, Rong-Jaye

doi:10.1142/s0129054198000167

Cited by 45 publications

(31 citation statements)

References 3 publications

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“…The (n, k)-star graph is regular of degree n − 1 and has connectivity n − 1 [9]. The (n, k)-star graph has n!…”

Section: Other Interconnection Networkmentioning

confidence: 99%

A general algorithm for detecting faults under the comparison diagnosis model

Stewart

2010

2010 IEEE International Symposium on Parallel &Amp; Distributed Processing (IPDPS)

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractWe develop a widely applicable algorithm to solve the fault diagnosis problem in certain distributed-memory multiprocessor systems in which there are a limited number of faulty processors. In particular, we prove that if the underlying graph G = (V, E) forming the interconnection network has connectivity no less than its diagnosability δ and can be partitioned into enough connected components of large enough size then given a syndrome of test results under the comparison diagnosis model resulting from some set of faulty nodes of size at most δ, we can find the actual set of faulty nodes with time complexity O(∆N ), where ∆ is the maximal degree of any node of the graph and N is the number of nodes.

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“…The (n, k)-star graph is regular of degree n − 1 and has connectivity n − 1 [9]. The (n, k)-star graph has n!…”

Section: Other Interconnection Networkmentioning

confidence: 99%

A general algorithm for detecting faults under the comparison diagnosis model

Stewart

2010

2010 IEEE International Symposium on Parallel &Amp; Distributed Processing (IPDPS)

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“…S is illustrated in Figure 1. = with α internal cycles and β external cycles are computed by the following formulas [1], [2].…”

Section: Preliminariesmentioning

confidence: 99%

“…n nodes for an n-star. Some works have been done on this graph, such as basic properties [1], [2], [3], embeddability [3], broadcasting algorithms [4] ,and so on.…”

Section: Introductionmentioning

confidence: 99%

Optimum Broadcasting Algorithms in (n, k)-Star Graphs Using Spanning Trees

Li¹,

Chen

Xiang

et al. 2007

Lecture Notes in Computer Science

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Abstract. In a multiprocessor network, sending a packet typically refers to start-up time and transmission time. To optimize these two times, as opposed to earlier solutions, a spanning tree and multiple spanning trees are constructed to solve four types of broadcasting problems in an (n, k)-star graph: one-to-all or all-to-all broadcasting with either one-port or all-port communication model, respectively. Since the proposed spanning tree has an optimal height, both oneto-all and all-to-all broadcasting algorithms achieve nearly optimal start-up time and transmission time under all-port model and one-port model, and optimal transmission time under one-port model. By using multiple spanning trees, both one-to-all and all-to-all algorithms achieve nearly optimal transmission time under all-port model and one-port model.

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“…S n,k has better scalability and it preserves many attractive properties of S n , such as node symmetry, distance, diameter, hierarchical structure, and fault-free shortest routing [1,4,12]. Recent research results on broadcasting [11], topological properties [5], fault-tolerant connectivity [9,15] and weak-vertex-pancyclicity [3] demonstrate that S n,k is a very powerful network.…”

Section: Introductionmentioning

confidence: 99%

AN ADAPTIVE HEURISTIC ALGORITHM WITH THE PROBABILISTIC SAFETY VECTOR FOR FAULT-TOLERANT ROUTING ON THE (n, k)-STAR GRAPH

Chiu

Huang

Yang

et al. 2014

Int. J. Found. Comput. Sci.

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The (n, k)-star graph is a generalization of the n-star graph. It has better scalability than the n-star graph and holds some good properties compared with the hypercube. This paper focuses on the design of the fault-tolerant routing algorithm for the (n, k)-star graph. We adopt the idea of collecting the limited global information used for routing on the n-star graph to the (n, k)-star graph. In the preliminary version of this paper, we built the probabilistic safety vector (PSV) with modified cycle patterns and developed the routing algorithm to decide the fault-free routing path with the help of PSV. Afterwards, we observed that the routing performance of PSV gets worse as the percentage of fault nodes increases, especially it exceeds 25%. In order to improve the routing performance with more faulty nodes, an adaptive method of threshold assignment for the PSV is also proposed. The performance is judged by the average length of routing paths. Compared with distance first search and safety level, PSV with dynamic threshold gets the best performance in the simulations.

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TOPOLOGICAL PROPERTIES OF THE (n,k)-STAR GRAPH

Cited by 45 publications

References 3 publications

A general algorithm for detecting faults under the comparison diagnosis model

A general algorithm for detecting faults under the comparison diagnosis model

Optimum Broadcasting Algorithms in (n, k)-Star Graphs Using Spanning Trees

AN ADAPTIVE HEURISTIC ALGORITHM WITH THE PROBABILISTIC SAFETY VECTOR FOR FAULT-TOLERANT ROUTING ON THE (n, k)-STAR GRAPH

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