Distributed approximation algorithms for finding 2-edge-connected subgraphs

Authors:
Sven O. Krumke;Peter Merz;Tim Nonner;Katharina Rupp
Affiliations:
Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany;Department of Computer Science, University of Kaiserslautern, Kaiserslautern, Germany;Department of Computer Science, Albert-Ludwigs-University Freiburg, Freiburg im Breisgau, Germany;Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany
Venue:
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
Year:
2007

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Abstract

We consider the distributed construction of a minimum weight 2- edge-connected spanning subgraph (2-ECSS) of a given weighted or unweighted graph. A 2-ECSS of a graph is a subgraph that, for each pair of vertices, contains at least two edge-disjoint paths connecting these vertices. The problem of finding a minimum weight 2-ECSS is NP-hard and a natural extension of the distributed MST construction problem, one of the most fundamental problems in the area of distributed computation. We present a distributed 3/2-approximation algorithm for the unweighted 2-ECSS construction problem that requires O(n) communication rounds and O(m) messages. Moreover, we present a distributed 3-approximation algorithm for the weighted 2-ECSS construction problem that requires O(nlogn) communication rounds and O(nlog2 n+m) messages.