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Computational Complexity of the \(r\)-visibility Guard Set Problem for Polyominoes

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Discrete and Computational Geometry and Graphs (JCDCGG 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8845))

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Abstract

We study the art gallery problem when the instance is a polyomino, which is the union of connected unit squares. It is shown that locating the minimum number of guards with \(r\)-visibility in a polyomino with holes is NP-hard. Here, two points \(u\) and \(v\) on a polyomino are r-visible if the orthogonal bounding rectangle for \(u\) and \(v\) lies entirely within the polyomino. As a corollary, locating the minimum number of guards with \(r\)-visibility in an orthogonal polygon with holes is NP-hard.

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Authors and Affiliations

  1. Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Chuzo Iwamoto & Toshihiko Kume

Authors
  1. Chuzo Iwamoto
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  2. Toshihiko Kume
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Correspondence to Chuzo Iwamoto .

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Editors and Affiliations

  1. Tokyo University of Science, Tokyo, Japan

    Jin Akiyama

  2. The University of Electro-Communications, Tokyo, Japan

    Hiro Ito

  3. Tokai University, Tokyo, Japan

    Toshinori Sakai

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Iwamoto, C., Kume, T. (2014). Computational Complexity of the \(r\)-visibility Guard Set Problem for Polyominoes. In: Akiyama, J., Ito, H., Sakai, T. (eds) Discrete and Computational Geometry and Graphs. JCDCGG 2013. Lecture Notes in Computer Science(), vol 8845. Springer, Cham. https://doi.org/10.1007/978-3-319-13287-7_8

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  • DOI: https://doi.org/10.1007/978-3-319-13287-7_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-13286-0

  • Online ISBN: 978-3-319-13287-7

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