A polyhedral study of the diameter constrained minimum spanning tree problem∗

This paper provides a study of integer linear programming formulations for the diameter con-strained spanning tree problem (DMSTP) in the natural space of edge design variables. Afterpresenting a straightforward model based on the well known jump inequalities a new stronger familyof circular-jump inequalities is introduced. These inequalities are further generalized in two ways:either by increasing the number of partitions defining a jump, or by combining jumps with cutsets.Most of the proposed new inequalities are shown to define facets of the DMSTP polyhedron undervery mild conditions. Currently best known lower bounds for the DMSTP are obtained from anextended formulation on a layered graph using the concept of central nodes/edges. The new familiesof inequalities are shown not to be implied by this layered graph formulation.