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Combinatorial Aspects of Move-Up Crews for Spreading Processes on Networks

In: Operations Research Proceedings 2008

Author

Listed:
  • Marco Laumanns

    (Institute for Operations Research, ETH Zurich)

  • Rico Zenklusen

    (Institute for Operations Research, ETH Zurich)

Abstract

Summary Spreading processes on networks can often be mapped onto network reliability problems. The computational complexity of computing the probability that the spreading process reaches some given subset K of the nodes is well studied as it reduces to the classical K-terminal reliability problem. Often one is not interested in a particular set K, but more global properties of the spreading process, such as the expected spreading size or the probability of a large spreading. We show that the direct Monte Carlo approach is an FPRAS for the expected spreading size, but unless NP ⊆ BPP, there is no randomized constant-factor approximation for the probability of large spreadings. When nodes are weighted to represent their importance, we show that estimating the expected spreading impact is of the same computational complexity as estimating s-t reliability.

Suggested Citation

  • Marco Laumanns & Rico Zenklusen, 2009. "Combinatorial Aspects of Move-Up Crews for Spreading Processes on Networks," Springer Books, in: Bernhard Fleischmann & Karl-Heinz Borgwardt & Robert Klein & Axel Tuma (ed.), Operations Research Proceedings 2008, chapter 93, pages 575-580, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-00142-0_93
    DOI: 10.1007/978-3-642-00142-0_93
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