Fast minor testing in planar graphs

  • Authors:

  • Isolde Adler;Frederic Dorn;Fedor V. Fomin;Ignasi Sau;Dimitrios M. Thilikos

  • Affiliations:

  • Institut für Informatik, Goethe-Universität, Frankfurt, Germany;Department of Informatics, University of Bergen, Norway;Department of Informatics, University of Bergen, Norway;Department of Computer Science, Technion, Haifa, Israel;Department of Mathematics, National and Kapodistrian University of Athens, Greece

  • Venue:
  • ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
  • Year:
  • 2010

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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 Cu and Cv. 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 2O(h)ċn+O(n2ċlog 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.