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

Cristina Bazgan, Sonia Toubaline, Daniel Vanderpooten
2012 Computers & Operations Research  
Efficient determination of the k most vital edges for the minimum spanning tree problem. 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
more » ... , 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.
doi:10.1016/j.cor.2012.02.023 fatcat:blexyofnn5djjmeaazcb4nflsq