A New Necessary Condition for Shortest Path Routing

In shortest path routing, traffic is routed along shortest paths defined by link weights. However, not all path systems are feasible in that they can be realized in this way. This is something which needs to be taken into account when searching for a set of paths that minimize capacity consumption. In this paper, we discuss a new necessary condition that can be used during search to prune infeasible path systems. The condition can be expressed using linear inequalities, or used in constraint programming, where its simple definition is convenient for the efficient implementation of propagation. Experiments on networks from the SNDLib benchmark show that this condition has strong pruning capabilities.