Graph minors. XIII: the disjoint paths problem
Journal of Combinatorial Theory Series B
Approximations for the disjoint paths problem in high-diameter planar networks
Journal of Computer and System Sciences
The edge-disjoint path problem is NP-complete for series-parallel graphs
Discrete Applied Mathematics - Special issue on selected papers from First Japanese-Hungarian Symposium for Discrete Mathematics and its Applications
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Journal of Computer and System Sciences
Edge-Disjoint Paths in Planar Graphs
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Multicommodity flow, well-linked terminals, and routing problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
An Approximation Algorithm for the Disjoint Paths Problem in Even-Degree Planar Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Edge-Disjoint Paths in Planar Graphs with Constant Congestion
SIAM Journal on Computing
The edge disjoint paths problem in Eulerian graphs and 4-edge-connected graphs
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Maximum Edge-Disjoint Paths in Planar Graphs with Congestion 2
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
The disjoint paths problem in quadratic time
Journal of Combinatorial Theory Series B
Hi-index | 0.00 |
In this article, we study an approximation algorithm for the maximum edge-disjoint paths problem. In this 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(log2 n)-approximation algorithm given by Kleinberg [2005] for Eulerian planar graphs. Our result also generalizes the result by Chekuri et al. [2004, 2005] who gave an O(log n)-approximation algorithm for the maximum edge-disjoint paths problem with congestion two when an input graph is planar.