Feasibility issues in shortest-path routing with traffic flow split

In English In the Internet’s autonomous systems packets are routed on shortest paths to their destinations. A related problem is how to find an admissible traffic routing configuration using paths that can be generated by a system of weights assigned to IP links. This problem is NP-hard. It can be formulated as a mixed-integer program and attempted with a branch-and-cut algorithm if effective cuts (valid inequalities) can be derived. In this paper we discuss admissibility of shortest-path routing configurations represented by binary variables specifying whether or not a particular link is on a shortest path to a particular destination. We present a linear programming problem for testing routing admissibility and derive solutions of this problem which characterize non-admissible routing configurations.