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On the Resiliency of Randomized Routing Against Multiple Edge Failures

Authors Marco Chiesa, Andrei Gurtov, Aleksander Madry, Slobodan Mitrovic, Ilya Nikolaevskiy, Michael Shapira, Scott Shenker

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Marco Chiesa
Andrei Gurtov
Aleksander Madry
Slobodan Mitrovic
Ilya Nikolaevskiy
Michael Shapira
Scott Shenker

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Marco Chiesa, Andrei Gurtov, Aleksander Madry, Slobodan Mitrovic, Ilya Nikolaevskiy, Michael Shapira, and Scott Shenker. On the Resiliency of Randomized Routing Against Multiple Edge Failures. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 134:1-134:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.ICALP.2016.134

Abstract

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.

Subject Classification

Keywords
  • Randomized
  • Routing
  • Resilience
  • Connectivity
  • Arborescenses

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