Results 221 to 230 of about 3,964 (242)

On the rectilinear art gallery problem

2005
It is shown that [n/4] point guards are always sufficient and sometimes necessary to watch a rectilinear polygon with an arbitrary number of holes, where n is the total number of vertices.
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A Novel Efficient Approach for Solving the Art Gallery Problem

2013
In this paper, we consider the Art Gallery Problem (AGP) that asks for the minimum number of guards placed in a polygon to oversee the whole polygon. The AGP is known to be NP-hard even for very restricted special cases. This paper describes a primal-dual algorithm based on continuous optimization techniques for solving large-scale instances of the Art
Alexander Kröller, Mahdi Moeini, Christiane Schmidt 0001   +2 more
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The Art Gallery Problem is existsR-complete

2017
We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational geometry. Given a simple polygon P and an integer k, the goal is to decide if there exists a set G of k guards ...
Abrahamsen, Mikkel, Adamaszek, Anna, Miltzow, Till   +2 more
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An Exact Algorithm for the Discrete Chromatic Art Gallery Problem

2014
Recently introduced in [1], the Chromatic Art Gallery Problem (CAGP) is related to the well known Art Gallery Problem to the extent that given a polygon P, a set of guards within P that satisfies a particular property is sought. Define a proper coloring of a guard set that covers the polygon as a color assignment in which any two guards receive ...
Maurício J. O. Zambon, Pedro J. de Rezende, Cid C. de Souza   +2 more
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The Art Gallery Problem is ∃ℝ-complete

Journal of the ACM, 2022
Mikkel Abrahamsen, Anna Adamaszek, Tillmann Miltzow   +2 more
exaly  

Chromatic Art Gallery Problem with <i>r</i>-Visibility is NP-Complete

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2021
Chuzo Iwamoto
exaly  

Computational Complexity of the Vertex-to-Point Conflict-Free Chromatic Art Gallery Problem

IEICE Transactions on Information and Systems, 2023
Chuzo Iwamoto
exaly  

The Art Gallery Problem

Math Horizons, 1994
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Approximation Algorithms for Art Gallery Problems in Polygons and Terrains

2010
In this survey paper, we present an overview of approximation algorithms that are designed for art gallery problems in polygons and terrains.
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Solving the art gallery problem

2021
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