Information Processing Letters
Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Orderings and some combinatorial optimization problems with geometric applications
Orderings and some combinatorial optimization problems with geometric applications
Art gallery theorems and algorithms
Art gallery theorems and algorithms
On the rectilinear art gallery problem
Proceedings of the seventeenth international colloquium on Automata, languages and programming
A Graph-Coloring Result and Its Consequences For Polygon-Guarding Problems
SIAM Journal on Discrete Mathematics
An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The art gallery theorem: its variations, applications and algorithmic aspects
The art gallery theorem: its variations, applications and algorithmic aspects
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We consider guarding a city of kvertical 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.