TY - CHAP
T1 - On the Resiliency of Randomized Routing Against Multiple Edge Failures
AU - Chiesa, Marco
AU - Gurtov, Andrei
AU - Madry, Aleksander
AU - MitroviÄ‡, Slobodan
AU - Nikolaevskiy, Ilya
AU - Shapira, Michael
AU - Shenker, Scott
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Arborescenses
KW - Connectivity
KW - Randomized
KW - Resilience
KW - Routing
U2 - 10.4230/LIPIcs.ICALP.2016.134
DO - 10.4230/LIPIcs.ICALP.2016.134
M3 - Chapter
SN - 978-3-95977-013-2
T3 - Leibniz International Proceedings in Informatics
SP - 1
EP - 15
BT - 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)
A2 - Chatzigiannakis, Ioannis
A2 - Mitzenmacher, Michael
A2 - Rabani, Yuval
A2 - Sangiorgi, Davide
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ER -