A 4-Approximation Algorithm for Guarding 1.5-Dimensional Terrains
نویسنده
چکیده
In the 1.5-dimensional terrain guarding problem we are given as input an x-monotone chain (the terrain) and asked for the minimum set of guards (points on the terrain) such that every point on the terrain is seen by at least one guard. It has recently been shown that the 1.5-dimensional terrain guarding problem is approximable to within a constant factor [3,7], though no attempt has been made to minimize the approximation factor. We give a 4-approximation algorithm for the 1.5D terrain guarding problem that runs in quadratic time. Our algorithm is faster, simpler, and has a better worst-case approximation factor than previous algorithms.
منابع مشابه
The Complexity of Guarding Terrains
A set G of points on a 1.5-dimensional terrain, also known as an x-monotone polygonal chain, is said to guard the terrain if any point on the terrain is seen by a point in G. Two points on the terrain see each other if and only if the line segment between them is never strictly below the terrain. The minimum terrain guarding problem asks for a minimum guarding set for the given input terrain. W...
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