A Fixed Parameter Tractable Approximation Scheme for the Optimal Cut Graph of a Surface

  • Vincent Cohen-Addad
  • Arnaud de Mesmay
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)

Abstract

Given a graph G cellularly embedded on a surface Σ of genus g, a cut graph is a subgraph of G such that cutting Σ along G yields a topological disk. We provide a fixed parameter tractable approximation scheme for the problem of computing the shortest cut graph, that is, for any ε > 0, we show how to compute a (1 + ε) approximation of the shortest cut graph in time f(ε, g)n3.

Our techniques first rely on the computation of a spanner for the problem using the technique of brick decompositions, to reduce the problem to the case of bounded tree-width. Then, to solve the bounded tree-width case, we introduce a variant of the surface-cut decomposition of Rué, Sau and Thilikos, which may be of independent interest.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Vincent Cohen-Addad
    • 1
  • Arnaud de Mesmay
    • 2
  1. 1.Département d’informatiqueÉcole normale supérieureParisFrance
  2. 2.IST AustriaViennaAustria

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