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arXiv · 1304.4207

The planar directed k-Vertex-Disjoint Paths problem is fixed-parameter tractable

Marek Cygan·Dániel Marx·Marcin Pilipczuk·Michał Pilipczuk
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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.

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Marek Cygan, Dániel Marx, Marcin Pilipczuk, Michał Pilipczuk. 2013-04-15. The planar directed k-Vertex-Disjoint Paths problem is fixed-parameter tractable. https://arxiv.org/abs/1304.4207

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