Static and dynamic source locations in undirected networks

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...

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Vydáno v:TOP Ročník 23; číslo 3; s. 619 - 646
Hlavní autoři: Turner, Lara, Groß, Dwi Poetranto, Hamacher, Horst W., Krumke, Sven O.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.10.2015
Témata:
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Industrial and Production Engineering
Insurance
Invited Paper
Management
Operations Research/Decision Theory
Optimization
Statistics for Business
Fully polynomial-time approximation scheme
Linear algorithm
(Minimal) deficient set
Matroid
(Dual) greedy algorithm
Single cover problem
Plural cover problem
Tree network
NP-hardness
90B10
Pseudo-polynomial algorithm
Source location problem
Dynamic flow
90B80
ISSN:1134-5764, 1863-8279
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Popis
Shrnutí: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.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-015-0395-7