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Better Approximation Schemes for Disk Graphs

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Algorithm Theory – SWAT 2006 (SWAT 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4059))

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Abstract

We consider Maximum Independent Set and Minimum Vertex Cover on disk graphs. We propose an asymptotic FPTAS for Minimum Vertex Cover on disk graphs of bounded ply. This scheme can be extended to an EPTAS on arbitrary disk graphs, improving on the previously known PTAS [8]. We introduce the notion of level density for disk graphs, which is a generalization of the notion of ply. We give an asymptotic FPTAS for Maximum Independent Set on disk graphs of bounded level density, which is also a PTAS on arbitrary disk graphs. The schemes are a geometric generalization of Baker’s EPTASs for planar graphs [3].

This research was supported by the Bsik project BRICKS.

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Author information

Authors and Affiliations

  1. CWI, Kruislaan 413, 1098 SJ, Amsterdam, The Netherlands

    Erik Jan van Leeuwen

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  1. Erik Jan van Leeuwen
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Editor information

Editors and Affiliations

  1. MADALGO, Department of Computer Science, University of Aarhus, Denmark

    Lars Arge

  2. Institute of Mathematics and Computer Science, University of Latvia, Raiņa bulvāris 29, Rīga, LV-1459, Latvia

    Rusins Freivalds

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van Leeuwen, E.J. (2006). Better Approximation Schemes for Disk Graphs. In: Arge, L., Freivalds, R. (eds) Algorithm Theory – SWAT 2006. SWAT 2006. Lecture Notes in Computer Science, vol 4059. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11785293_30

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  • DOI: https://doi.org/10.1007/11785293_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-35753-7

  • Online ISBN: 978-3-540-35755-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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