TY - INPR
A1 - Turner, Lara
A1 - Hamacher, Horst W.
T1 - Universal Shortest Paths
N2 - 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.
T3 - Report in Wirtschaftsmathematik (WIMA Report) - 128
KW - Combinatorial optimization
KW - shortest path problem
KW - universal objective function
Y1 - 2010
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/2230
UR - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:hbz:386-kluedo-16624
ER -