On the Computational Complexity of Policy Routing Márton Zubor 1,3 , Attila Kőrösi 1,2,4 , and András Gulyás 1,2,4 and Gábor Rétvári 1,2,5 1 Budapest University of Technology and Economics, Hungary 2 Department of Telecommunication and Mediainformatics 3 Department of Algebra 4 Hungarian Academy of Science (MTA) Information system research group 5 MTA-BME Future Internet Research Group {zubor, korosi, gulyas, retvari}@tmit.bme.hu Abstract. 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 re- visit the theoretic underpinnings of policy routing in the light of the new requirements. We show that certain simple but plausible algebraic prop- erties 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. Keywords: policy routing, path selection, routing algebras, computational com- plexity 1 Introduction Policy routing is the art and science of determining optimal forwarding paths under complex operational constraints. Originally in shortest path routing the rule was simply to pick the least cost path with respect to some additive link weights, but network operators have increasingly turned towards more sophisti- cated policies like path reliability and resilience [17], bandwidth and perceived congestion [8,16], business relations and service level agreements [2], etc. These routing policies, and the computational complexity of the path selection prob- lem thereof, are well-understood today, thanks to the theory of routing alge- bras [4, 5, 14, 15]. Recently, however, new routing architectures have surfaced for which today’s algebraic routing theory does not provide adequate complexity characterization. Data centers, for instance, operate over starkly optimized topologies and services, defined by rules significantly more customized than allowed by classical routing policies. With the emergence of Software Defined Networks (SDN), furthermore, operators now enjoy complete freedom to shape their routing preferences [9]. A perfect example of how the seemingly simple problem of calculating the preferred path between two nodes can become surprisingly complicated is the upcoming A. Gravey, Y. Kermarrec (Eds.) 1 EUNICE 2014