On the resiliency of randomized routing against multiple edge failures

QC 20180207
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 Static-Routing-Resiliency problem. For any k-connected graph, we show a surprisingly simple randomized algorithm that has expected number of hops O(|V|k) if at most k-1 edges fail, which reduces to O(|V|) if only a fraction t of the links fail (where t < 1 is a constant). Furthermore, our algorithm is deterministic if the routing does not encounter any failed link.

In:43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016: Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing9783959770132

By the author/editor: Chiesa, Marco, 1 ...; Gurtov, A.; Madry, A.; Mitrovic, S.; Nikolaevskiy, I.; Schapira, M.; show more...; Shenker, S.; show less...

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NATURAL SCIENCES: NATURAL SCIENCES; and Computer and Inf ...; and Computer Science ...

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