## Heuristics for the K-Cardinality Tree and Subgraph Problems

• In this paper we consider the problem of finding in a given graph a minimal weight subtree of connected subgraph, which has a given number of edges. These NP-hard combinatorial optimization problems have various applications in the oil industry, in facility layout and graph partitioning. We will present different heuristic approaches based on spanning tree and shortest path methods and on an exact algorithm solving the problem in polynomial time if the underlying graph is a tree. Both the edge- and node weighted case are investigated and extensive numerical results on the behaviour of the heuristics compared to optimal solutions are presented. The best heuristic yielded results within an error margin of less than one percent from optimality for most cases. In a large percentage of tests even optimal solutions have been found.

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Verfasserangaben: Matthias Ehrgott, Horst. W. Hamacher, J. Freitag, F. Maffioli urn:nbn:de:hbz:386-kluedo-4930 Report in Wirtschaftsmathematik (WIMA Report) (8) Preprint Englisch 1996 1996 Technische Universität Kaiserslautern 03.04.2000 K-cardinality trees Asia Pacific Journal of Operational Research, vol 14, no 1, May 1997 Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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