Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs

Authors Éric Colin de Verdiére, Alexander Schrijver

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Éric Colin de Verdiére
Alexander Schrijver

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Éric Colin de Verdiére and Alexander Schrijver. Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs. In 25th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 1, pp. 181-192, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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 $s_1,ldots,s_k$ be vertices incident with~$s$; let $t_1,ldots,t_k$ 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 $O(knlog n)$ time.
  • Algorithm
  • planar graph
  • disjoint paths
  • shortest path


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