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.
|Original language||American English|
|Title of host publication||43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016|
|Editors||Yuval Rabani, Ioannis Chatzigiannakis, Davide Sangiorgi, Michael Mitzenmacher|
|Publisher||Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing|
|State||Published - 1 Aug 2016|
|Event||43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016 - Rome, Italy|
Duration: 12 Jul 2016 → 15 Jul 2016
|Name||Leibniz International Proceedings in Informatics, LIPIcs|
|Conference||43rd International Colloquium on Automata, Languages, and Programming, ICALP 2016|
|Period||12/07/16 → 15/07/16|
Bibliographical notePublisher Copyright:
© Marco Chiesa, Andrei Gurtov, Aleksander Madry, Slobodan Mitrovic, Ilya Nikolaevskiy.