## New heuristics for the minimum fundamental cut basis problem

• Given an undirected connected network and a weight function finding a basis of the cut space with minimum sum of the cut weights is termed Minimum Cut Basis Problem. This problem can be solved, e.g., by the algorithm of Gomory and Hu [GH61]. If, however, fundamentality is required, i.e., the basis is induced by a spanning tree T in G, the problem becomes NP-hard. Theoretical and numerical results on that topic can be found in Bunke et al. [BHMM07] and in Bunke [Bun06]. In the following we present heuristics with complexity O(m log n) and O(mn), where n and m are the numbers of vertices and edges respectively, which obtain upper bounds on the aforementioned problem and in several cases outperform the heuristics of Schwahn [Sch05].

Author: Alexander J. Perez Tchernov, Anne M. Schwahn urn:nbn:de:hbz:386-kluedo-15041 Report in Wirtschaftsmathematik (WIMA Report) (112) Preprint English 2007 2007 Technische Universität Kaiserslautern 2007/07/24 NP; algorithm ; cut ; data structure ; fundamental cut ; heuristic ; minimum fundamental cut basis Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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