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This work is licensed under the Creative Commons Attribution-NoDerivs License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nd/3
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Shortest Vertex-Disjoint Two-Face Paths in Planar Graphs ` ERIC COLIN DE VERDIERE, Ecole Normale Sup rieure and CNRS e ALEXANDER SCHRIJVER, Centrum voor Wiskunde en Informatica 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(kn log n) time. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical algorithms and problems Computations on discrete structures; routing and layout; G.2.2 [Discrete Mathematics]: Graph Theory Graph algorithms; network problems; path and circuit problems General Terms: Algorithms, Performance, Theory Additional Key Words and Phrases: Algorithm, disjoint paths, planar graph, shortest path ACM Reference Format: Colin de Verdi` re, E. and Schrijver, A. 2011. Shortest vertex-disjoint two-face paths in planar graphs. ACM e Trans. Algor. 7, 2, Article 19 (March 2011), 12 pages. DOI = 10.1145/1921659.1921665 http://doi.acm.org/10.1145/1921659.1921665 1. INTRODUCTION The vertex-disjoint paths
ACM Transactions on Algorithms (TALG) – Association for Computing Machinery
Published: Mar 1, 2011
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