An O(log n)-approximation algorithm for the disjoint paths problem in Eulerian planar graphs and 4-edge-connected planar graphs

Authors:
Ken-Ichi Kawarabayashi;Yusuke Kobayashi
Affiliations:
National Institute of Informatics, Tokyo, Japan;Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan
Venue:
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Year:
2010

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Abstract

In this paper, we study an approximation algorithm for the maximum edge-disjoint paths problem. In the maximum edge-disjoint paths problem, we are given a graph and a collection of pairs of vertices, and the objective is to find the maximum number of pairs that can be connected by edge-disjoint paths. We give an O(log n)-approximation algorithm for the maximum edge-disjoint paths problem when an input graph is either 4-edge-connected planar or Eulerian planar. This improves an O(log2n)-approximation algorithm given by Kleinberg [10] for Eulerian planar graphs. Our result also generalizes the result by Chekuri, Khanna and Shepherd [2,3] who gave an O(log n)-approximation algorithm for the edge-disjoint paths problem with congestion 2 when an input graph is planar.