منابع مشابه
Exact Algorithms for Terrain Guarding
Given a 1.5-dimensional terrain T , also known as an x-monotone polygonal chain, the Terrain Guarding problem seeks a set of points of minimum size on T that guards all of the points on T . Here, we say that a point p guards a point q if no point of the line segment pq is strictly below T . The Terrain Guarding problem has been extensively studied for over 20 years. In 2005 it was already estab...
متن کاملApproximation algorithms for terrain guarding
We present approximation algorithms and heuristics for several variations of terrain guarding problems, where we need to guard a terrain in its entirety by a minimum number of guards. Terrain guarding has applications in telecommunications, namely in the setting up of antenna networks for wireless communication. Our approximation algorithms transform the terrain guarding instance into a MINIMUM...
متن کاملAn Approximation Scheme for Terrain Guarding
We obtain a polynomial time approximation scheme for the terrain guarding problem improving upon several recent constant factor approximations. Our algorithm is a local search algorithm inspired by the recent results of Chan and Har-Peled [2] and Mustafa and Ray [15]. Our key contribution is to show the existence of a planar graph that appropriately relates the local and global optimum.
متن کاملAltitude Terrain Guarding and Guarding Uni-Monotone Polygons
We show that the problem of guarding an x-monotone terrain from an altitude line and the problem of guarding a uni-monotone polygon are equivalent. We present a polynomial time algorithm for both problems, and show that the cardinality of a minimum guard set and the cardinality of a maximum witness set coincide. Thus, uni-monotone polygons are perfect; this result also extends to monotone mount...
متن کاملEfficient Algorithms for Guarding or Illuminating the Surface of a Polyhedral Terrain
We present eecient polynomial time algorithms that place bn=2c vertex guards which cover the surface of an n-vertex polyhedral terrain, and similarly, bn=3c edge guards which cover the surface of an n-vertex polyhedral terrain. The time complexity of both algorithms, dominated by the cost of nding a maximum matching in a graph, is O(n 3=2).
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ژورنال
عنوان ژورنال: ACM Transactions on Algorithms
سال: 2018
ISSN: 1549-6325,1549-6333
DOI: 10.1145/3186897