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On the Hardness of Some Geometric Optimization Problems with Rectangles

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Combinatorial Optimization and Applications (COCOA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11949))

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Abstract

We study the Set Cover, Hitting Set, Piercing Set, Independent Set, Dominating Set problems, and discrete versions (Discrete Independent Set and Discrete Dominating Set) for geometric instances in the plane. We focus on certain restricted classes of geometric objects, including axis-parallel lines, strips, and rectangles. For rectangles, we consider the cases in which the rectangles are (i) anchored on a horizontal line, (ii) anchored on two lines (either two parallel lines or one vertical and one horizontal line), and (iii) stabbed by a horizontal line. Some versions of these problems have been studied previously; we focus here on the open cases, for which no complexity results were known.

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Acknowledgements

We would like to thank Joseph S. B. Mitchell for fruitful discussions in the early stages of this paper.

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Authors and Affiliations

  1. Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat, India

    Supantha Pandit

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  1. Supantha Pandit
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Correspondence to Supantha Pandit .

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Editors and Affiliations

  1. Georgia State University, Atlanta, GA, USA

    Yingshu Li

  2. Florida Atlantic University, Boca Raton, FL, USA

    Mihaela Cardei

  3. Kennesaw State University, Marietta, GA, USA

    Yan Huang

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Pandit, S. (2019). On the Hardness of Some Geometric Optimization Problems with Rectangles. In: Li, Y., Cardei, M., Huang, Y. (eds) Combinatorial Optimization and Applications. COCOA 2019. Lecture Notes in Computer Science(), vol 11949. Springer, Cham. https://doi.org/10.1007/978-3-030-36412-0_34

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  • DOI: https://doi.org/10.1007/978-3-030-36412-0_34

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-36411-3

  • Online ISBN: 978-3-030-36412-0

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