Static and dynamic source locations in undirected networks

Lara Turner (), Dwi Groß (), Horst Hamacher () and Sven Krumke ()

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2015, vol. 23, issue 3, 619-646

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

Keywords: Source location problem; Single cover problem; Matroid; (Dual) greedy algorithm; (Minimal) deficient set; Plural cover problem; Tree network; Linear algorithm; Pseudo-polynomial algorithm; Fully polynomial-time approximation scheme; Dynamic flow; NP-hardness; 90B10; 90B80 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11750-015-0395-7

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