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International Workshop on Graph-Theoretic Concepts in Computer Science

WG 2007: Graph-Theoretic Concepts in Computer Science pp 280–291Cite as

How to Use Planarity Efficiently: New Tree-Decomposition Based Algorithms

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4769))

Abstract

We prove new structural properties for tree-decompositions of planar graphs that we use to improve upon the runtime of tree-decomposition based dynamic programming approaches for several NP-hard planar graph problems. We give for example the fastest algorithm for Planar Dominating Set of runtime 3tw ·n O(1), when we take the treewidth tw as the measure for the exponential worst case behavior. We also introduce a tree-decomposition based approach to solve non-local problems efficiently, such as Planar Hamiltonian Cycle in runtime 6tw ·n O(1). From any input tree-decomposition, we compute in time O(nm) a tree-decomposition with geometric properties, which decomposes the plane into disks, and where the graph separators form Jordan curves in the plane.

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Authors and Affiliations

  1. Department of Informatics, University of Bergen, PO Box 7800, 5020 Bergen, Norway

    Frederic Dorn

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  1. Frederic Dorn
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Editor information

Andreas Brandstädt Dieter Kratsch Haiko Müller

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© 2007 Springer-Verlag Berlin Heidelberg

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Dorn, F. (2007). How to Use Planarity Efficiently: New Tree-Decomposition Based Algorithms. In: Brandstädt, A., Kratsch, D., Müller, H. (eds) Graph-Theoretic Concepts in Computer Science. WG 2007. Lecture Notes in Computer Science, vol 4769. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74839-7_27

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  • DOI: https://doi.org/10.1007/978-3-540-74839-7_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-74838-0

  • Online ISBN: 978-3-540-74839-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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