# A Linear-Time Approximation Algorithm for the Orthogonal Terrain Guarding Problem

In this paper, we consider the 1.5-dimensional orthogonal terrain guarding problem. In this problem, we assign an x-monotone chain T because each edge is either horizontal or vertical, and determine the minimal number of vertex guards for all vertices of T. A vertex vi sees a point p on T if the line segment connecting vi to p is on or above T. We provide an optimal algorithm with O(n) for a subproblem of the orthogonal terrain guarding problem. In this subproblem, we determine the minimal number of vertex guards for all right(left) convex verteices of T. Finally, we provide a 2-approximation algorithm that solves the 1.5-dimensional orthogonal terrain guarding problem in O(n).

## Authors

• 2 publications
• 2 publications
• ### Continuous Terrain Guarding with Two-Sided Guards

Herein, we consider the continuous 1.5-dimensional(1.5D) terrain guardin...
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• ### Vertex guarding for dynamic orthogonal art galleries

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• ### Optimal Construction for Time-Convex Hull with Two Orthogonal Highways in the L1-metric

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• ### A note on minimal art galleries

We will consider some extensions of the polygonal art gallery problem. I...
09/19/2019 ∙ by Eryk Lipka, et al. ∙ 0

• ### A 3/4 Differential Approximation Algorithm for Traveling Salesman Problem

In this paper, we consider differential approximability of the traveling...
12/28/2020 ∙ by Yuki Amano, et al. ∙ 0