Disjoint paths in symmetric digraphs

Authors:
A. Jarry;S. Pérennes
Affiliations:
Projet Mascotte, INRIA Sophia-Antipolis, 2004 route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex, France;Projet Mascotte, INRIA Sophia-Antipolis, 2004 route des Lucioles, B.P. 93, 06902 Sophia Antipolis Cedex, France
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 11
Cited 1

Multicommodity flows in certain planar directed networks

Discrete Applied Mathematics - Computational combinatiorics
Weak three-linking in Eulerian digraphs

SIAM Journal on Discrete Mathematics
Graph minors. XIII: the disjoint paths problem

Journal of Combinatorial Theory Series B
NP-completeness of some edge-disjoint paths problems

Discrete Applied Mathematics
Connectivity and network flows

Handbook of combinatorics (vol. 1)
Graph classes: a survey

Graph classes: a survey
Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph

Journal of the ACM (JACM)
A Polynomial Solution to the Undirected Two Paths Problem

Journal of the ACM (JACM)
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
The subgraph homeomorphism problem

STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The equivalence of theorem proving and the interconnection problem

ACM SIGDA Newsletter

Multiflows in symmetric digraphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

Given a number of requests @?, we propose a polynomial-time algorithm for finding @? disjoint paths in a symmetric directed graph. It is known that the problem of finding @?=2 disjoint paths in a directed graph is NP-hard [S. Fortune, J. Hopcroft, J. Wyllie, The directed subgraph homeomorphism problem, Journal of Theoretical Computer Science 10 (2) (1980) 111-121]. However, by studying minimal solutions it turns out that only a finite number of configurations are possible in a symmetric digraph. We use Robertson and Seymour's polynomial-time algorithm [N. Robertson, P. D. Seymour, Graph minors xiii. The disjoint paths problem, Journal of Combinatorial Theory B (63) (1995) 65-110] to check the feasibility of each configuration.