Shortest vertex-disjoint two-face paths in planar graphs

Authors:
Éric Colin De Verdière;Alexander Schrijver
Affiliations:
École Normale Supérieure and CNRS, Paris, France;Centrum voor Wiskunde en Informatica, Amsterdam, Netherlands
Venue:
ACM Transactions on Algorithms (TALG)
Year:
2011

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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 s1,…,sk be vertices incident with s let t1,…,tk be vertices incident with t. We give an algorithm to compute k pairwise vertex-disjoint paths connecting the pairs (si,ti) in G, with minimal total length, in O(knlog n) time.