Loop-Free Integrated Forwarding and Routing with Gradients

Selecting optimum paths subject to multiple constraints is known to be an NP-complete problem for either additive or multiplicative constraints, and very few approaches have been advanced that operate distributively or address more than two constraints. On the other hand, forwarding loops are known to occur in dynamic networks even when routing tables are loop-free at every instant. We propose and analyze IFRoG (Integrated Forwarding and Routing with Gradients), the first approach for loop-free multi-constrained forwarding and routing based on gradient vectors. IFRoG is based on a fully distributed algorithm for the computation of loop-free routes using vectors of gradients that specify path performance for a given additive or multiplicative performance metric (e.g., latency or bandwidth). Data packets are forwarded on a hop-by-hop basis and carry gradient values used to eliminate forwarding loops. We show that IFRoG renders valid loop-free multi-constrained paths to destinations within a finite time and that no data packet can traverse a forwarding loop independently of the state of the forwarding tables maintained by routers. Furthermore, we show that IFRoG has smaller complexity than approaches that require each router to maintain complete network state at each router.