Complexity of resilient network optimisation

Authors

  • Mateusz Żotkiewicz,

    Corresponding author
    1. Institute of Telecommunications, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warszawa, Poland
    2. TELECOM & Management SudParis, 9 rue Charles Fourier, 91011 Evry, France
    • Institute of Telecommunications, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warszawa, Poland.
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  • Michał Pióro,

    1. Institute of Telecommunications, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warszawa, Poland
    2. Department of Electrical and Information Technology, Lund University, S-221 00 Lund, Sweden
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  • Artur Tomaszewski

    1. Institute of Telecommunications, Warsaw University of Technology, ul. Nowowiejska 15/19, 00-665 Warszawa, Poland
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  • A previous version of this paper was presented at the 5th Polish-German Teletraffic Symposium (PGTS 2008), Berlin, Germany.

Abstract

Path restoration (PR) is one of the basic mechanisms for securing telecommunication networks against failures. In the paper, we discuss the complexity of certain variants of a multi-commodity flow network optimisation problem in directed graphs related to state-independent path restoration mechanisms. We demonstrate that most variants of the considered problem are equation image-hard. Depending on the variant, we show how the problem can be reduced either from the partition problem or from the problem of finding an arc-disjoint pair of paths that connect two distinct pairs of nodes. We also demonstrate that at the same time the considered problem is difficult to approximate. The complexity results of the paper are important as they can help to devise proper algorithms for resilient network design tools. Copyright © 2009 John Wiley & Sons, Ltd.

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