Computing the Shortest Network under a Fixed Topology

shortest network interconnecting a given set of points under a fixed topology can be computed by solving a linear programming problem whose size is bounded by a polynomial in the number of terminals and the number of legal orientations. When the given topology is restricted to a Steiner topology, our result implies that the Steiner minimum tree under a given Steiner topology can be computed in polynomial time in any given uniform orientation metric with A legal orientations for any fixed integer A > 2. This settles an open problem posed in a recent paper [3].