Efficient determination of the k most vital edges for the minimum spanning tree problem

  • Authors:

  • Cristina Bazgan;Sonia Toubaline;Daniel Vanderpooten

  • Affiliations:

  • Université Paris-Dauphine, LAMSADE Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France and Institut Universitaire de France, France;Université Paris-Dauphine, LAMSADE Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France;Université Paris-Dauphine, LAMSADE Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2012

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Abstract

We study in this paper the problem of finding in a graph a subset of k edges whose deletion causes the largest increase in the weight of a minimum spanning tree. We propose for this problem an explicit enumeration algorithm whose complexity, when compared to the current best algorithm, is better for general k but very slightly worse for fixed k. More interestingly, unlike in the previous algorithms, we can easily adapt our algorithm so as to transform it into an implicit enumeration algorithm based on a branch and bound scheme. We also propose a mixed integer programming formulation for this problem. Computational results show a clear superiority of the implicit enumeration algorithm both over the explicit enumeration algorithm and the mixed integer program.