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Computational Complexity of the Chromatic Art Gallery Problem for Orthogonal Polygons

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WALCOM: Algorithms and Computation (WALCOM 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12049))

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Abstract

The art gallery problem is to find a set of guards who together can observe every point of the interior of a polygon P. We study a chromatic variant of the problem, where each guard is assigned one of k distinct colors. The chromatic art gallery problem is to find a guard set for P such that no two guards with the same color have overlapping visibility regions. We study the decision version of this problem for orthogonal polygons with r-visibility when the number of colors is \(k=2\). Here, two points are r-visible if the smallest axis-aligned rectangle containing them lies entirely within the polygon. In this paper, it is shown that determining whether there is an r-visibility guard set for an orthogonal polygon with holes such that no two guards with the same color have overlapping visibility regions is NP-hard when the number of colors is \(k=2\).

This work was supported by JSPS KAKENHI Grant Number 16K00020.

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Authors and Affiliations

  1. Hiroshima University, Higashi-Hiroshima, 739-8521, Japan

    Chuzo Iwamoto & Tatsuaki Ibusuki

Authors
  1. Chuzo Iwamoto
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  2. Tatsuaki Ibusuki
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Correspondence to Chuzo Iwamoto .

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Editors and Affiliations

  1. Department of CSE, BUET, Dhaka, Bangladesh

    M. Sohel Rahman

  2. Mathematical Informatics, University of Tokyo, Tokyo, Japan

    Kunihiko Sadakane

  3. School of Computing, National University of Singapore, Singapore, Singapore

    Wing-Kin Sung

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Iwamoto, C., Ibusuki, T. (2020). Computational Complexity of the Chromatic Art Gallery Problem for Orthogonal Polygons. In: Rahman, M., Sadakane, K., Sung, WK. (eds) WALCOM: Algorithms and Computation. WALCOM 2020. Lecture Notes in Computer Science(), vol 12049. Springer, Cham. https://doi.org/10.1007/978-3-030-39881-1_13

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  • DOI: https://doi.org/10.1007/978-3-030-39881-1_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-39880-4

  • Online ISBN: 978-3-030-39881-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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