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Determining the Conditional Diagnosability of k-Ary n-Cubes Under the MM* Model

  • Conference paper
Structural Information and Communication Complexity (SIROCCO 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6796))

Abstract

Processor fault diagnosis plays an important role for measuring the reliability of multiprocessor systems, and the diagnosability of many well-known interconnection networks has been investigated widely. Conditional diagnosability is a novel measure of diagnosability, which is introduced by Lai et al., by adding an additional condition that any faulty set cannot contain all the neighbors of any vertex in a system. The class of k-ary n-cubes contains as special cases many topologies important to parallel processing, such as rings, hypercubes, and tori. In this paper, we study some topological properties of the k-ary n-cube, denoted by \(Q^k_n\). Then we apply them to show that the conditional diagnosability of \(Q^k_n\) under the comparison diagnosis model is \(t_c(Q^k_n)=6n-5\) for k ≥ 4 and n ≥ 4.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan, 701, Taiwan

    Sun-Yuan Hsieh & Chi-Ya Kao

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  1. Sun-Yuan Hsieh
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  2. Chi-Ya Kao
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Editors and Affiliations

  1. INRIA, Bordeau Sud-Ouest Research Center, 351 cours de la Libération, 33400, Talence cedex, France

    Adrian Kosowski

  2. Department of Computer Science and Communication Engineering, Kyushu University, 744, Motooka, 819-0395, Fukuoka, Japan

    Masafumi Yamashita

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Hsieh, SY., Kao, CY. (2011). Determining the Conditional Diagnosability of k-Ary n-Cubes Under the MM* Model. In: Kosowski, A., Yamashita, M. (eds) Structural Information and Communication Complexity. SIROCCO 2011. Lecture Notes in Computer Science, vol 6796. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22212-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-22212-2_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22211-5

  • Online ISBN: 978-3-642-22212-2

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