English

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

Computational Geometry 2018-05-10 v2

Abstract

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).

Keywords

Cite

@article{arxiv.1804.11088,
  title  = {A Linear-Time Approximation Algorithm for the Orthogonal Terrain Guarding Problem},
  author = {Wei-Yu Lai and Tien-Ruey Hsiang},
  journal= {arXiv preprint arXiv:1804.11088},
  year   = {2018}
}
R2 v1 2026-06-23T01:39:43.064Z