Minimum Cycle Bases for Network Graphs

  • Authors:

  • Franziska Berger;Peter Gritzmann;Sven de Vries

  • Affiliations:

  • Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching bei München, Germany;Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching bei München, Germany;Zentrum Mathematik, Technische Universität München, Boltzmannstraße 3, D-85747 Garching bei München, Germany

  • Venue:
  • Algorithmica
  • Year:
  • 2004

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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|.