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Minimising K-Dominating Set in Arbitrary Network Graphs

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Advanced Data Mining and Applications (ADMA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 8347))

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Abstract

A self-stabilizing algorithm, after transient faults hit the system and place it in some arbitrary global state, recovers in finite time without external (e.g., human) intervention. A k-dominating set in a distributed system is a set of processors such that each processor outside the set has at least k neighbors in the set. In the past, a few self-stabilizing algorithms for minimal k-dominating set (MKDS) have been obtained. However, the presented self-stabilizing algorithms for MKDS work for either trees or a minimal 2-dominating set. Recently a self-stabilizing algorithm for MKDS in arbitrary graphs under a central daemon has been investigated. But so far, there is no algorithm for the MKDS problem in arbitrary graphs that works under a distributed daemon. In this paper, we propose a self-stabilizing algorithm for finding a MKDS under a distributed daemon model when operating in any general network graph. We further verify the correctness of the proposed algorithm (Algorithm MKDS) and prove that the worst case convergence time of the algorithm from any arbitrary initial state is O(n 2) steps where n is the number of nodes in the network.

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Author information

Authors and Affiliations

  1. Department of Maths and Computing, University of Southern Queensland, QLD, 4350, Australia

    Guangyuan Wang, Hua Wang, Xiaohui Tao & Ji Zhang

  2. School of Applied Mathematics, Beijing Normal University, Zhuhai, 519085, China

    Jinhua Zhang

Authors
  1. Guangyuan Wang
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  2. Hua Wang
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  3. Xiaohui Tao
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  4. Ji Zhang
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  5. Jinhua Zhang
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Editor information

Editors and Affiliations

  1. US Air Force Office of Scientific Research, 106-0032, Tokyo, Japan

    Hiroshi Motoda

  2. School of Computer Science and Technology, Zhejiang University, 310027, Hangzhou, China

    Zhaohui Wu

  3. Faculty of Engineering and Information Technology, University of Technology, Chippendale, 2008, Sydney, NSW, Australia

    Longbing Cao

  4. Department of Computing Science, Edmonton, University of Alberta, T6G 2E8, Canada

    Osmar Zaiane

  5. College of Computer Science and Technology, Zhejiang University, Hangzhou, China

    Min Yao

  6. School of Computer Science, Fudan University, 200433, Shanghai, China

    Wei Wang

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© 2013 Springer-Verlag Berlin Heidelberg

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Wang, G., Wang, H., Tao, X., Zhang, J., Zhang, J. (2013). Minimising K-Dominating Set in Arbitrary Network Graphs. In: Motoda, H., Wu, Z., Cao, L., Zaiane, O., Yao, M., Wang, W. (eds) Advanced Data Mining and Applications. ADMA 2013. Lecture Notes in Computer Science(), vol 8347. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53917-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-53917-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-53916-9

  • Online ISBN: 978-3-642-53917-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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