Traffic Engineering with ECMP: An Algorithmic Perspective

To efficiently exploit network resources operators do traffic engineering (TE), i.e., adapt the routing of traffic to the prevailing demands. TE in large IP networks typically relies on configuring static link weights and splitting traffic between the resulting shortest-paths via the Equal-Cost-MultiPath (ECMP) mechanism. Yet, despite its vast popularity, crucial operational aspects of TE via ECMP are still little-understood from an algorithmic viewpoint. We embark upon a systematic algorithmic study of TE with ECMP. We first consider the standard “splittable-flow” model of TE with ECMP, put forth in [18]. We settle a long-standing open question by proving that, in general, even approximating the optimal link-weight configuration for ECMP within any constant ratio is an intractable feat. We also initiate the analytical study of TE with ECMP on specific network topologies and, in particular, datacenter networks. We prove that while TE with ECMP remains suboptimal and computationallyhard for hypercube networks, ECMP can, in contrast, provably achieve optimal traffic flow for the important category of folded Clos networks. We next investigate the approximability of TE with ECMP in the more realistic “unsplittable-flow” model and present upper and lower bounds for scheduling “elephant” flows on top of ECMP (as in, e.g., Hedera [4]). Our results complement and shed new light on past experimental and empirical studies of the performance of TE with ECMP.