Minimum weight spanning trees with bounded diameter

Let G be a simple graph with non-negative edge weights. Determining a minimum weight spanning tree is a fundamental problem that arises in network design and as a subproblem in many combinatorial optimization problems such as vehicle routing. In some applications, it is necessary to restrict the diameter of the spanning tree and thus one is interested in the problem : Find, in a given weighted graph G, a minimum weight spanning tree of diameter at most D. This problem is known to be NP-complete for D 2:: 4. In this paper we present a mixed integer linear programming formulation and discuss some solution procedures.