## 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 |
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URN (permanent link): | urn:nbn:de:hbz:386-kluedo-15041 |

Serie (Series number): | Report in Wirtschaftsmathematik (WIMA Report) (112) |

Document Type: | Preprint |

Language of publication: | English |

Year of Completion: | 2007 |

Year of Publication: | 2007 |

Publishing Institute: | Technische Universität Kaiserslautern |

Date of the Publication (Server): | 2007/07/24 |

Tag: | NP; algorithm ; cut ; data structure ; fundamental cut ; heuristic ; minimum fundamental cut basis |

Faculties / Organisational entities: | Fachbereich Mathematik |

DDC-Cassification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |

Licence (German): | Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011 |