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International Colloquium on Automata, Languages, and Programming

ICALP 2001: Automata, Languages and Programming pp 261–272Cite as

Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems

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Part of the book series: Lecture Notes in Computer Science ((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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Author information

Authors and Affiliations

  1. Wilhelm-Schickard-Institut für Informatik, Universität Tübingen, Sand 13, 72076, Tübingen, Fed. Rep. of Germany

    Jochen Alber, Henning Fernau & Rolf Niedermeier

Authors
  1. Jochen Alber
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  2. Henning Fernau
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  3. Rolf Niedermeier
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Editor information

Editors and Affiliations

  1. Departament de Llenguatges i Sistemes Informátics, Univ. Politècnica de Catalunya, C/Jordi Girona Salgado 1-3, 08034, Barcelona, Spain

    Fernando Orejas

  2. Computer Technology Institute (CTI), University of Patras, 61 Riga Feraiou street, 26221, Patras, Greece

    Paul G. Spirakis

  3. Institute of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584, CH, Utrecht, The Netherlands

    Jan van Leeuwen

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© 2001 Springer-Verlag Berlin Heidelberg

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Alber, J., Fernau, H., Niedermeier, R. (2001). Parameterized Complexity: Exponential Speed-Up for Planar Graph Problems. In: Orejas, F., Spirakis, P.G., van Leeuwen, J. (eds) Automata, Languages and Programming. ICALP 2001. Lecture Notes in Computer Science, vol 2076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48224-5_22

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  • DOI: https://doi.org/10.1007/3-540-48224-5_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42287-7

  • Online ISBN: 978-3-540-48224-6

  • eBook Packages: Springer Book Archive

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