Spanning trees with variable degree bounds

In this paper, we describe a minimum spanning tree problem with variable degree bounds. The objective is to find a minimum cost spanning tree where the cost of each edge depends on the degree of its end nodes and where edges with a higher cost enable higher degrees. This problem is motivated by the design of wireless networks, where each wireless link, operating on a given frequency channel, must have a transmission system able to cope with both the distance between its end nodes and the interference added by channels of the other links starting/ending on its end nodes. We propose three classes of models using different sets of variables and compare from a theoretical perspective as well as from a computational point of view, the models and the corresponding linear programming relaxations. The computational results show that some of the proposed models are able to solve to optimality instances with 100 and 200 nodes and different scenarios.