On Some City Guarding Problems

  • Lichen Bao
  • Sergey Bereg
  • Ovidiu Daescu
  • Simeon Ntafos
  • Junqiang Zhou
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

Abstract

We consider guarding a city of k vertical buildings, each having a rectangular base, by placing guards only at vertices. The aim is to use the smallest number of guards. The problem is a 2.5D variant of the traditional art gallery problem, and finds applications in urban security.

We give upper and lower bounds on the number of guards needed for a few versions of the problem. Specifically, we prove that \(\lfloor\frac{2(k-1)}{3}\rfloor + 1\) guards are always sufficient and sometimes necessary to guard all roofs, and \(1 + k + \lfloor \frac{k}{2}\rfloor\) guards are always sufficient to guard the roofs, walls, and the ground, while each roof has at least one guard on it.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Lichen Bao
    • 1
  • Sergey Bereg
    • 1
  • Ovidiu Daescu
    • 1
  • Simeon Ntafos
    • 1
  • Junqiang Zhou
    • 1
  1. 1.Department of Computer Science Erik Jonsson School of Engineering & Computer ScienceThe University of Texas at DallasRichardsonUSA

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