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Determining the Smallest k Such That G Is k-Outerplanar

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Algorithms – ESA 2007 (ESA 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4698))

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Abstract

The outerplanarity index of a planar graph G is the smallest k such that G has a k-outerplanar embedding. We show how to compute the outerplanarity index of an n-vertex planar graph in O(n 2) time, improving the previous best bound of O(k 3 n 2). Using simple variations of the computation we can determine the radius of a planar graph in O(n 2) time and its depth in O(n 3) time.

We also give a linear-time 4-approximation algorithm for the outerplanarity index and show how it can be used to solve maximum independent set and several other NP-hard problems faster on planar graphs with outerplanarity index within a constant factor of their treewidth.

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Authors and Affiliations

  1. Institut für Informatik, Universität Augsburg, 86135 Augsburg, Germany

    Frank Kammer

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  1. Frank Kammer
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Editor information

Lars Arge Michael Hoffmann Emo Welzl

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Kammer, F. (2007). Determining the Smallest k Such That G Is k-Outerplanar. In: Arge, L., Hoffmann, M., Welzl, E. (eds) Algorithms – ESA 2007. ESA 2007. Lecture Notes in Computer Science, vol 4698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75520-3_33

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  • DOI: https://doi.org/10.1007/978-3-540-75520-3_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75519-7

  • Online ISBN: 978-3-540-75520-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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