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Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems

  • Jochen Alber
  • Henning Fernau
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2076)

Abstract

A parameterized problem is fixed parameter tractable if it admits a solving algorithm whose running time on input instance (I,k) is f(k) · |I|;α, where f is an arbitrary function depending only on k. Typically, f is some exponential function, e.g., f(k) = c k for constant c. We describe general techniques to obtain growth of the form f(k) = c k for a large variety of planar graph problems. The key to this type of algorithm is what we call the “Layerwise Separation Property” of a planar graph problem. Problems having this property include PLANAR VERTEX COVER, PLANAR INDEPENDENT SET, and PLANAR DOMINATING SET.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Jochen Alber
    • 1
  • Henning Fernau
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenFed. Rep. of Germany

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