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

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 (n 5/3(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.

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The authors acknowledge theDeutsche Forschungsgemeinschaft for supporting this research under grantMö 446/1-3

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Wagner, D., Weihe, K. A linear-time algorithm for edge-disjoint paths in planar graphs. Combinatorica 15, 135–150 (1995). https://doi.org/10.1007/BF01294465

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Mathematics Subject Classification (1991)

  • 05 C 85
  • 68 Q 35