A Novel Mathematical Model for the Unique Shortest Path Routing Problem

Link weights are the principal parameters of shortest path routing protocols, the most commonly used protocols for IP networks. The problem of optimally setting link weights for unique shortest path routing is addressed. Due to the complexity of the constraints involved, there exist challenges to formulate the problem properly, so that a solution algorithm may be developed which could prove to be more efficient than those already in existence. In this paper, a novel complete formulation with a polynomial number of constraints is first introduced and then mathematically proved to be correct. It is further illustrated that the formulation has advantages over a prior one in terms of both constraint structure and model size for a proposed decomposition method to solve the problem.