  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.
