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Fast Minor Testing in Planar Graphs

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Algorithms – ESA 2010 (ESA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6346))

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Abstract

Minor containment is a fundamental problem in Algorithmic Graph Theory, as numerous graph algorithms use it as a subroutine. A model of a graph H in a graph G is a set of disjoint connected subgraphs of G indexed by the vertices of H, such that if {u,v} is an edge of H, then there is an edge of G between components C u and C v . Graph H is a minor of G if G contains a model of H as a subgraph. We give an algorithm that, given a planar n-vertex graph G and an h-vertex graph H, either finds in time \(2^{\mathcal{O}(h)} \cdot n + \mathcal{O}(n^{2}\cdot \log n)\) a model of H in G, or correctly concludes that G does not contain H as a minor. Our algorithm is the first single-exponential algorithm for this problem and improves all previous minor testing algorithms in planar graphs. Our technique is based on a novel approach called partially embedded dynamic programming.

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Author information

Authors and Affiliations

  1. Institut für Informatik, Goethe-Universität, Frankfurt, Germany

    Isolde Adler

  2. Department of Informatics, University of Bergen, Norway

    Frederic Dorn & Fedor V. Fomin

  3. Department of Computer Science, Technion, Haifa, Israel

    Ignasi Sau

  4. Department of Mathematics, National and Kapodistrian, University of Athens, Greece

    Dimitrios M. Thilikos

Authors
  1. Isolde Adler
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  2. Frederic Dorn
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  3. Fedor V. Fomin
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  4. Ignasi Sau
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  5. Dimitrios M. Thilikos
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Editor information

Editors and Affiliations

  1. Department of Mathematics and Computing Science, TU Eindhoven, Eindhoven, The Netherlands

    Mark de Berg

  2. Institute for Computer Science, J.W. Goethe University, 60325, Frankfurt/Main, Germany

    Ulrich Meyer

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Adler, I., Dorn, F., Fomin, F.V., Sau, I., Thilikos, D.M. (2010). Fast Minor Testing in Planar Graphs. In: de Berg, M., Meyer, U. (eds) Algorithms – ESA 2010. ESA 2010. Lecture Notes in Computer Science, vol 6346. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15775-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-15775-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15774-5

  • Online ISBN: 978-3-642-15775-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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