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Covering and Packing of Rectilinear Subdivision

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WALCOM: Algorithms and Computation (WALCOM 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11355))

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Abstract

We study a class of geometric covering and packing problems for bounded closed regions on the plane. We are given a set of axis-parallel line segments that induce a planar subdivision with bounded (rectilinear) faces. We are interested in the following problems.  

(P1) Stabbing-Subdivision::

Stab all closed bounded faces by selecting a minimum number of points in the plane.

(P2) Independent-Subdivision::

Select a maximum size collection of pairwise non-intersecting closed bounded faces.

(P3) Dominating-Subdivision::

Select a minimum size collection of bounded faces such that every other face has a non-empty intersection (i.e., sharing an edge or a vertex) with some selected face.

  We show that these problems are \(\mathsf { NP }\)-hard. We even prove that these problems are \(\mathsf { NP }\)-hard when we concentrate only on the rectangular faces of the subdivision. Further, we provide constant factor approximation algorithms for the Stabbing-Subdivision problem.

S. Pandit—Partially supported by the Indo-US Science & Technology Forum (IUSSTF) under the SERB Indo-US Postdoctoral Fellowship scheme with grant number 2017/94, Department of Science and Technology, Government of India.

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Author information

Authors and Affiliations

  1. Indian Statistical Institute, Kolkata, India

    Satyabrata Jana

  2. Stony Brook University, Stony Brook, NY, USA

    Supantha Pandit

Authors
  1. Satyabrata Jana
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  2. Supantha Pandit
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Corresponding authors

Correspondence to Satyabrata Jana or Supantha Pandit .

Editor information

Editors and Affiliations

  1. Indian Institute of Technology Guwahati, Guwahati, India

    Gautam K. Das

  2. Indian Institute of Technology Guwahati, Guwahati, India

    Partha S. Mandal

  3. Indian Statistical Institute, Kolkata, India

    Krishnendu Mukhopadhyaya

  4. Gunma University, Kiryu, Japan

    Shin-ichi Nakano

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Jana, S., Pandit, S. (2019). Covering and Packing of Rectilinear Subdivision. In: Das, G., Mandal, P., Mukhopadhyaya, K., Nakano, Si. (eds) WALCOM: Algorithms and Computation. WALCOM 2019. Lecture Notes in Computer Science(), vol 11355. Springer, Cham. https://doi.org/10.1007/978-3-030-10564-8_30

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  • DOI: https://doi.org/10.1007/978-3-030-10564-8_30

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-10563-1

  • Online ISBN: 978-3-030-10564-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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