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Commercial backbone networks must continue to operate even when links and routers fail. Routing schemes such as OSPF, IS-IS, and MPLS reroute traffic, but they cannot guarantee that the resulting network will be congestion-free. As a result, backbone networks are grossly over-provisioned - sometimes running at a utilization below 10% so they can remain uncongested under failure. Yet even with such large over-provisioning, they still cannot guarantee to be uncongested, sometimes even with just a single failure. With our proposed approach, a network can be designed to tolerate an almost arbitrary number of failures, and guarantee no congestion, usually with an extremely small amount of over- provisioning. In a typical case, a 50 node network can continue to run congestion-free when any 5 links or routers fail, with only 10% over-provisioning. The key to the approach is Valiant Load-Balancing (VLB). VLB's path diversity allows it to tolerate k arbitrary failures in an N node network, with over-provisioning ratio of approximately k/N.