COCOON 2008: Computing and Combinatorics pp 600-610

# On Some City Guarding Problems

• Lichen Bao
• Sergey Bereg
• Ovidiu Daescu
• Simeon Ntafos
• Junqiang Zhou
Conference paper
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.

## Keywords

Parent Node Simple Polygon Incoming Edge Generic Trap Blue Edge
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## 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