A New Formulation for Spanning Trees

Spanning trees are fundamental structures in graph theory. Furthermore, computing them is a central part in many relevant algorithms, used in either practical or theoretical applications. The classical Minimum Spanning Tree problem is solvable in polynomial time but almost all of its variants are NP-Hard. In this paper, a novel polynomial size mixed integer linear programming formulation is introduced for spanning trees. This formulation is based on a new characterization we propose for acyclic graphs. Preliminary computational results show that this formulation is capable of solving small instances of the diameter constrained minimum spanning tree problem. It should be possible to strengthen the formulation to tackle larger instances of that problem. Additionally, our spanning tree formulation may prove to be a more effective model for some related applications.