The planar directed k-Vertex-Disjoint Paths problem is fixed-parameter tractable
Discrete Mathematics
2013-04-16 v1 Data Structures and Algorithms
Combinatorics
Abstract
Given a graph G and k pairs of vertices (s_1,t_1), ..., (s_k,t_k), the k-Vertex-Disjoint Paths problem asks for pairwise vertex-disjoint paths P_1, ..., P_k such that P_i goes from s_i to t_i. Schrijver [SICOMP'94] proved that the k-Vertex-Disjoint Paths problem on planar directed graphs can be solved in time n^{O(k)}. We give an algorithm with running time 2^{2^{O(k^2)}} n^{O(1)} for the problem, that is, we show the fixed-parameter tractability of the problem.
Cite
@article{arxiv.1304.4207,
title = {The planar directed k-Vertex-Disjoint Paths problem is fixed-parameter tractable},
author = {Marek Cygan and Dániel Marx and Marcin Pilipczuk and Michał Pilipczuk},
journal= {arXiv preprint arXiv:1304.4207},
year = {2013}
}
Comments
110 pages, 43 figures