On the Resiliency of Randomized Routing Against Multiple Edge Failures

We study the STATIC-ROUTING-RESILIENCY problem, motivated by routing on the Internet: Given a graph G = (V,E), a unique destination vertex d, and an integer constant c > 0, does there exist a static and destination-based routing scheme such that the correct delivery of packets from any source s to the destination d is guaranteed so long as (1) no more than c edges fail and (2) there exists a physical path from s to d? We embark upon a study of this problem by relating the edge-connectivity of a graph, i.e., the minimum number of edges whose deletion partitions G, to its resiliency. Following the success of randomized routing algorithms in dealing with a variety of problems (e.g., Valiant load balancing in the network design problem), we embark upon a study of randomized routing algorithms for the STATICROUTING-RESILIENCY problem. For any k-connected graph, we show a surprisingly simple randomized algorithm that has expected number of hopsO(|V |k) if at most k−1 edges fail, which reduces toO(|V |) if only a fraction α of the links fail (where α < 1 is a constant). Furthermore, our algorithm is deterministic if the routing does not encounter any failed link. 1998 ACM Subject Classification C.2.2 Network Protocols