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Minimum Cycle Bases for Network Graphs

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Abstract

The minimum cycle basis problem in a graph G = (V,E) is the task to construct a minimum length basis of its cycle vector space. A well-known algorithm by Horton of 1987 needs running time O(|V||E|2.376). We present a new combinatorial approach which generates minimum cycle bases in time O(\max{|E|3,|E||V|2log |V|}) with a space requirement of Θ(|E|2). This method is especially suitable for large sparse graphs of electric engineering applications since there, typically, |E| is close to linear in |V|.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching bei München, Germany

    Franziska Berger, Peter Gritzmann & Sven de Vries

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  1. Franziska Berger
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  2. Peter Gritzmann
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  3. Sven de Vries
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Correspondence to Franziska Berger, Peter Gritzmann or Sven de Vries.

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Berger, F., Gritzmann, P. & de Vries, S. Minimum Cycle Bases for Network Graphs. Algorithmica 40, 51–62 (2004). https://doi.org/10.1007/s00453-004-1098-x

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  • DOI: https://doi.org/10.1007/s00453-004-1098-x

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