Spanning Trees with Node Degree Dependent Costs and Knapsack Reformulations

The Degree constrained Minimum Spanning Tree Problem (DMSTP) consists in finding a minimal cost spanning tree such that every node has a degree no greater than a fixed value. We consider a generalization of the DMSTP with a more general objective function that includes modular costs associated to the degree of each node. We show how the problem can be viewed as the intersection of a spanning tree problem and a knapsack problem. We present several linear programming models, based on the previous decompositions, together with some valid inequalities and compare their respective linear programming relaxations using random instances.