Computational complexity of art gallery problems
IEEE Transactions on Information Theory
Art gallery theorems and algorithms
Art gallery theorems and algorithms
Sweeping simple polygons with a chain of guards
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Art gallery theorems for guarded guards
Computational Geometry: Theory and Applications
Allocating Vertex π-Guards in Simple Polygons via Pseudo-Triangulations
Discrete & Computational Geometry
Maximizing the guarded boundary of an Art Gallery is APX-complete
Computational Geometry: Theory and Applications
A pseudopolynomial time O(log n)-approximation algorithm for art gallery problems
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
A note on the perimeter of fat objects
Computational Geometry: Theory and Applications
The art gallery theorem for simple polygons in terms of the number of reflex and convex vertices
Information Processing Letters
Triangulating and guarding realistic polygons
Computational Geometry: Theory and Applications
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Art gallery problems have been extensively studied over the last decade and have found different type of applications. Normally the number of sides of a polygon or the general shape of the polygon is used as a measure of the complexity of the problem. In this paper we explore another measure of complexity, namely, the number of guards required to guard the boundary, or the walls, of the gallery. We prove that if nguards are necessary to guard the walls of an art gallery, then an additional team of at most 4n茂戮驴 6 will guard the whole gallery. This result improves a previously known quadratic bound, and is a step towards a possibly optimal value of n茂戮驴 2 additional guards. The proof is algorithmic, uses ideas from graph theory, and is mainly based on the definition of a new reduction operator which recursively eliminates the simple parts of the polygon. We also prove that every gallery with cconvex vertices can be guarded by at most 2c茂戮驴 4 guards, which is optimal.