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arXiv · 0802.2845

Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs

Eric Colin De Verdière·Alexander Schrijver
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Abstract

Let $G$ be a directed planar graph of complexity $n$, each arc having a nonnegative length. Let $s$ and $t$ be two distinct faces of $G$; let $s_1,...,s_k$ be vertices incident with $s$; let $t_1,...,t_k$ be vertices incident with $t$. We give an algorithm to compute $k$ pairwise vertex-disjoint paths connecting the pairs $(s_i,t_i)$ in $G$, with minimal total length, in $O(kn\log n)$ time.

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Eric Colin De Verdière, Alexander Schrijver. 2008-02-20. Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs. https://arxiv.org/abs/0802.2845

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