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Optimal Network Decontamination with Threshold Immunity

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Algorithms and Complexity (CIAC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7878))

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Abstract

We consider the monotone connected graph search problem, that is, the problem of decontaminating a network infected by a mobile virus, using as few mobile cleaning agents as possible and avoiding recontamination. After a cleaning agent has left a vertex v, this vertex will become recontaminated if m or more of its neighbours are infected, where m ≥ 1 is a threshold parameter of the system. In the literature, the value of m has been limited to m = 1 or to the strict majority of the neighbours of the nodes.

In this paper, we consider this problem for any integer value m ≥ 1. We direct our investigation to widely used interconnection networks, namely meshes, hypercubes, and trees. For each of these classes of networks, we establish matching upper and lower bounds on the number of agents necessary to decontaminate with threshold m. The upper bound proofs are constructive: we present optimal decontamination protocols; we also show that these protocols are optimal or near-optimal in terms of number of moves.

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Author information

Authors and Affiliations

  1. Ottawa University, Canada

    Paola Flocchini

  2. University of Pisa, Italy

    Fabrizio Luccio & Linda Pagli

  3. Carleton University, Canada

    Nicola Santoro

Authors
  1. Paola Flocchini
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  2. Fabrizio Luccio
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  3. Linda Pagli
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  4. Nicola Santoro
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Editor information

Editors and Affiliations

  1. School of Engineering, Department of Computer Engineering and Informatics, University of Patras, 265 00, Patras, Greece

    Paul G. Spirakis

  2. LSI Department, Edif Omega, Universitat Politècnica de Catalunya, Campus Nord, Jordi Girona 1-3, 08034, Barcelona, Spain

    Maria Serna

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Flocchini, P., Luccio, F., Pagli, L., Santoro, N. (2013). Optimal Network Decontamination with Threshold Immunity. In: Spirakis, P.G., Serna, M. (eds) Algorithms and Complexity. CIAC 2013. Lecture Notes in Computer Science, vol 7878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38233-8_20

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  • DOI: https://doi.org/10.1007/978-3-642-38233-8_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38232-1

  • Online ISBN: 978-3-642-38233-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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