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Connected Guards in Orthogonal Art Galleries

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Computational Science and Its Applications — ICCSA 2003 (ICCSA 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2669))

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Abstract

In this paper we consider a variation of the Art Gallery Problem for orthogonal polygons. A set of points G in a polygon P n is a connected guard set for P n provided that is a guard set and the visibility graph of the set of guards G in P n is connected. The polygon P n is orthogonal provided each interior angle is 90° or 270°. First we use a coloring argument to prove that the minimum number of connected guards which are necessary to watch any orthogonal polygon with n sides is n/2 — 2. This result was originally established by induction by Hernández-Peñalver. Then we prove a new result for art galleries with holes: we show that n/2 — h connected guards are always sufficient to watch an orthogonal art gallery with n walls and h holes. This result is sharp when n = 4h + 4. We also construct galleries that require at least n/2 — h — 1 connected guards, for all n and h.

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Author information

Authors and Affiliations

  1. Mathematics Department, Southern Connecticut State University, New Haven, CT, 06515

    Val Pinciu

Authors
  1. Val Pinciu
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Editor information

Editors and Affiliations

  1. Army High Performance Computing Research Center, USA University of Minessota Department of Computer Science and Engineering, MN, 55455, USA

    Vipin Kumar

  2. Department of Computer Science, University of Calgary, Calgary, AB, T2N1N4, Canada

    Marina L. Gavrilova

  3. Heuchera Technologies Inc., 122 9251-8Yonge Street, Richmond Hill, ON, Canada, L4C 9T3

    Chih Jeng Kenneth Tan

  4. School of Computer Science, The Queen’s University of Belfast, Belfast, BT7 1NN, Northern Ireland UK

    Chih Jeng Kenneth Tan

  5. Département d’informatique et de recherche opérationelle Montréal, Université de Montréal, Québec, H3C 3J7, Canada

    Pierre L’Ecuyer

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© 2003 Springer-Verlag Berlin Heidelberg

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Pinciu, V. (2003). Connected Guards in Orthogonal Art Galleries. In: Kumar, V., Gavrilova, M.L., Tan, C.J.K., L’Ecuyer, P. (eds) Computational Science and Its Applications — ICCSA 2003. ICCSA 2003. Lecture Notes in Computer Science, vol 2669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44842-X_90

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  • DOI: https://doi.org/10.1007/3-540-44842-X_90

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40156-8

  • Online ISBN: 978-3-540-44842-6

  • eBook Packages: Springer Book Archive

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