Efficient algorithms for finding the k most vital edges for the minimum spanning tree problem

  • Authors:

  • Cristina Bazgan;Sonia Toubaline;Daniel Vanderpooten

  • Affiliations:

  • Université Paris-Dauphine, LAMSADE, Paris Cedex, France;Université Paris-Dauphine, LAMSADE, Paris Cedex, France;Université Paris-Dauphine, LAMSADE, Paris Cedex, France

  • Venue:
  • COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
  • Year:
  • 2011

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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 exploration 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.