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Universal Shortest Paths

  • We introduce the universal shortest path problem (Univ-SPP) which generalizes both - classical and new - shortest path problems. Starting with the definition of the even more general universal combinatorial optimization problem (Univ-COP), we show that a variety of objective functions for general combinatorial problems can be modeled if all feasible solutions have the same cardinality. Since this assumption is, in general, not satisfied when considering shortest paths, we give two alternative definitions for Univ-SPP, one based on a sequence of cardinality contrained subproblems, the other using an auxiliary construction to establish uniform length for all paths between source and sink. Both alternatives are shown to be (strongly) NP-hard and they can be formulated as quadratic integer or mixed integer linear programs. On graphs with specific assumptions on edge costs and path lengths, the second version of Univ-SPP can be solved as classical sum shortest path problem.

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Author:Lara Turner, Horst W. Hamacher
URN (permanent link):urn:nbn:de:hbz:386-kluedo-16624
Serie (Series number):Report in Wirtschaftsmathematik (WIMA Report) (128)
Document Type:Preprint
Language of publication:English
Year of Completion:2010
Year of Publication:2010
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2010/08/16
Tag:Combinatorial optimization; shortest path problem; universal objective function
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011