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Static and dynamic source locations in undirected networks

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  • Lara Turner
  • Dwi Groß
  • Horst Hamacher
  • Sven Krumke

Abstract

Results from source location in the form of single cover problems in static networks are reviewed and extended by new results for the most general problem with arbitrary demands and costs. The matroidal structure of the single covers is established and used in a new and simple validity proof of the dual greedy algorithm for static single cover problems. Moreover, a primal greedy algorithm is derived which uses a new procedure to find the collection of all minimal deficient sets. For static plural cover problems on trees two linear-time algorithms to solve simultaneous and non-simultaneous problems with uniform costs are presented; for the simultaneous scenario with non-uniform costs, a pseudo-polynomial algorithm is proposed which can be turned into a fully polynomial-time approximation scheme. In contrast to its static counterpart, the single cover problem in dynamic, i.e., time-varying networks is shown to be strongly NP-hard. For special cases of the network topology polynomial algorithms are presented. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • Lara Turner & Dwi Groß & Horst Hamacher & Sven Krumke, 2015. "Static and dynamic source locations in undirected networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 619-646, October.
    • Handle: RePEc:spr:topjnl:v:23:y:2015:i:3:p:619-646
    DOI: 10.1007/s11750-015-0395-7
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    References listed on IDEAS

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    3. V. Chvatal, 1979. "A Greedy Heuristic for the Set-Covering Problem," Mathematics of Operations Research, INFORMS, vol. 4(3), pages 233-235, August.
    4. Horst Hamacher & Stephanie Heller & Benjamin Rupp, 2013. "Flow location (FlowLoc) problems: dynamic network flows and location models for evacuation planning," Annals of Operations Research, Springer, vol. 207(1), pages 161-180, August.
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    Cited by:

    1. P. Heßler & H. W. Hamacher, 2016. "Sink location to find optimal shelters in evacuation planning," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 4(3), pages 325-347, September.

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