On the Computational Complexity of Policy Routing

With the advent of new network architectures, like Software Defined Networks, the rules governing the way traffic is routed through the network are becoming increasingly complex. In this paper, we revisit the theoretic underpinnings of policy routing in the light of the new requirements. We show that certain simple but plausible algebraic properties already induce intractable path selection instances, and we extend the algebraic description of policies for which the related path selection problem is guaranteed to be tractable with a new class, called polynomial finite algebras, which captures many real-life application domains.