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Scandinavian Workshop on Algorithm Theory

SWAT 2014: Algorithm Theory – SWAT 2014 pp 357–367Cite as

Approximation Algorithms for Hitting Triangle-Free Sets of Line Segments

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8503))

Abstract

We present polynomial time constant factor approximations on NP-Complete special instances of the Guarding a Set of Segments(GSS) problem. The input to the GSS problem consists of a set of line segments, and the goal is to find a minimum size hitting set of the given set of line segments. We consider the underlying planar graph on the set of intersection points as vertices and the edge set as pairs of vertices which are adjacent on a line segment. Our results are for the subclass of instances of GSS for which the underlying planar graph has girth at least 4. On this class of instances, we show that an optimum solution to the natural hitting set LP can be rounded to yield a 3-factor approximation to the optimum hitting set. The GSS problem remains NP-Complete on the sub-class of such instances. The main technique, that we believe could be quite general, is to round the hitting set LP optimum for special hypergraphs that we identify.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, Indian Institute of Technology Madras, India

    Anup Joshi & N. S. Narayanaswamy

Authors
  1. Anup Joshi
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  2. N. S. Narayanaswamy
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Editor information

Editors and Affiliations

  1. Tepper School of Business, Carnegie Mellon University, 15213, Pittsburgh, PA, USA

    R. Ravi

  2. DTU Informatics, 2800, Kongens Lyngby, Denmark

    Inge Li Gørtz

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Joshi, A., Narayanaswamy, N.S. (2014). Approximation Algorithms for Hitting Triangle-Free Sets of Line Segments. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_31

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  • DOI: https://doi.org/10.1007/978-3-319-08404-6_31

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08403-9

  • Online ISBN: 978-3-319-08404-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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