Combinatorica

, Volume 15, Issue 1, pp 135–150 | Cite as

A linear-time algorithm for edge-disjoint paths in planar graphs

  • Dorothea Wagner
  • Karsten Weihe
Article

Abstract

In this paper we discuss the problem of finding edge-disjoint paths in a planar, undirected graph such that each path connects two specified vertices on the boundary of the graph. We will focus on the “classical” case where an instance additionally fulfills the so-calledevenness-condition. The fastest algorithm for this problem known from the literature requiresO (n5/3(loglogn)1/3) time, wheren denotes the number of vertices. In this paper now, we introduce a new approach to this problem, which results in anO(n) algorithm. The proof of correctness immediately yields an alternative proof of the Theorem of Okamura and Seymour, which states a necessary and sufficient condition for solvability.

Mathematics Subject Classification (1991)

05 C 85 68 Q 35 

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Copyright information

© Akadémiai Kiadó 1995

Authors and Affiliations

  • Dorothea Wagner
    • 1
  • Karsten Weihe
    • 2
  1. 1.InformatikUniversität KonstanzKonstanzGermany
  2. 2.InformatikUniversität KonstanzKonstanzGermany

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