A primal branch-and-cut algorithm for the degree-constrained minimum spanning tree problem

Authors:
Markus Behle;Michael Jünger;Frauke Liers
Affiliations:
Max-Planck-Institut für Informatik, Saarbrücken, Germany;Universität zu Köln, Institut für Informatik, Köln, Germany;Universität zu Köln, Institut für Informatik, Köln, Germany
Venue:
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Year:
2007

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Abstract

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.