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International Conference on Combinatorial Optimization and Applications

COCOA 2019: Combinatorial Optimization and Applications pp 601–612Cite as

On Conflict-Free Chromatic Guarding of Simple Polygons

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

Abstract

We study the problem of colouring the vertices of a polygon, such that every viewer can see a unique colour. The goal is to minimize the number of colours used. This is also known as the conflict-free chromatic guarding problem with vertex guards, and is motivated, e.g., by the problem of radio frequency assignment to sensors placed at the polygon vertices. We study the scenario in which viewers can be all points of the polygon (such as a mobile robot which moves in the interior of the polygon). We efficiently solve the related problem of minimizing the number of guards and approximate (up to only an additive error) the number of colours required in the special case of polygons called funnels. As a corollary we sketch an upper bound of \(O(\log ^2 n)\) colours on n-vertex weak visibility polygons which generalizes to all simple polygons.

O. Çağırıcı—Supported by the Czech Science Foundation, project no. 17-00837S.

S. K. Ghosh—Supported by SERB, Government of India through a grant under MATRICS.

P. Hliněný—Supported by the Czech Science Foundation, project no. 17-00837S.

B. Roy—A significant part of the work was done while the author was affiliated to the Faculty of Informatics of Masaryk University.

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Author information

Authors and Affiliations

  1. Faculty of Informatics of Masaryk University, Brno, Czech Republic

    Onur Çağırıcı & Petr Hliněný

  2. Ramakrishna Mission Vivekananda University, Kolkata, India

    Subir Kumar Ghosh

  3. Indian Institute of Technology Kharagpur, Kharagpur, India

    Bodhayan Roy

Authors
  1. Onur Çağırıcı
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  2. Subir Kumar Ghosh
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  3. Petr Hliněný
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  4. Bodhayan Roy
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Corresponding author

Correspondence to Petr Hliněný .

Editor information

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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Çağırıcı, O., Ghosh, S.K., Hliněný, P., Roy, B. (2019). On Conflict-Free Chromatic Guarding of Simple Polygons. 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_49

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  • DOI: https://doi.org/10.1007/978-3-030-36412-0_49

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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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