A Primal Branch-and-Cut Algorithm for the Degree-Constrained Minimum Spanning Tree Problem

  • Markus Behle
  • Michael Jünger
  • Frauke Liers
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4525)


The degree-constrained minimum spanning tree (DCMST) is relevant in the design of networks. It consists of finding a spanning tree whose nodes do not exceed a given maximum degree and whose total edge length is minimum. We design a primal branch-and-cut algorithm that solves instances of the problem to optimality. Primal methods have not been used extensively in the past, and their performance often could not compete with their standard ‘dual’ counterparts. We show that primal separation procedures yield good bounds for the DCMST problem. On several instances, the primal branch-and-cut program turns out to be competitive with other methods known in the literature. This shows the potential of the primal method.


Span Tree Minimum Span Tree Cutting Plane Submodular Function Connectivity Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Markus Behle
    • 1
  • Michael Jünger
    • 2
  • Frauke Liers
    • 2
  1. 1.Max-Planck-Institut für Informatik, Stuhlsatzenhausweg 85, 66123 SaarbrückenGermany
  2. 2.Universität zu Köln, Institut für Informatik, Pohligstrasse 1, 50969 KölnGermany

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