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Guarding Thin Orthogonal Polygons Is Hard

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Fundamentals of Computation Theory (FCT 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8070))

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Abstract

An orthogonal polygon of P is called “thin” if the dual graph of the partition obtained by extending all edges of P towards its interior until they hit the boundary is a tree. We show that the problem of computing a minimum guard set for either a thin orthogonal polygon or only its vertices is NP-hard, indeed APX-hard, either for guards lying on the boundary or on vertices of the polygon. For guards lying anywhere in the polygon, we show that computing an optimal guard set for the vertices of such a polygon is NP-hard.

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Author information

Authors and Affiliations

  1. DCC & CMUP, Faculdade de Ciências, Universidade do Porto, Portugal

    Ana Paula Tomás

Authors
  1. Ana Paula Tomás
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Editor information

Editors and Affiliations

  1. Computer Science, University of Liverpool, Ashton Street, L69 3BX, Liverpool, UK

    Leszek Gąsieniec

  2. Department of Computer Science, University of Liverpool, United Kingdom

    Frank Wolter

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Tomás, A.P. (2013). Guarding Thin Orthogonal Polygons Is Hard. In: Gąsieniec, L., Wolter, F. (eds) Fundamentals of Computation Theory. FCT 2013. Lecture Notes in Computer Science, vol 8070. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40164-0_29

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  • DOI: https://doi.org/10.1007/978-3-642-40164-0_29

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40163-3

  • Online ISBN: 978-3-642-40164-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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