Guarding points on a terrain by watchtowers

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2025-06-26 DOI:10.1016/j.comgeo.2025.102210

Byeonguk Kang , Junhyeok Choi , Jeesun Han , Hee-Kap Ahn

引用次数: 0

Abstract

We study the problem of guarding points on an x-monotone polygonal chain, called a terrain, using k watchtowers. A watchtower is a vertical segment whose bottom endpoint lies on the terrain. A point on the terrain is visible from a watchtower if the line segment connecting the point and the top endpoint of the watchtower does not cross the terrain. Given a sequence of point sites lying on a terrain, we aim to partition the sequence into k contiguous subsequences and place k watchtowers on the terrain such that every point site in a subsequence is visible from the same watchtower and the maximum length of the watchtowers is minimized. We present efficient algorithms for two variants of the problem.

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用瞭望塔在地形上守卫点

利用k个瞭望塔研究了x-单调多边形链（称为地形）上点的守卫问题。瞭望塔是一个垂直的部分，其底部端点位于地形上。从瞭望塔上可以看到地形上的一个点，如果连接该点和瞭望塔顶端端点的线段没有穿过地形。给定一个位于地形上的点位置序列，我们的目标是将该序列划分为k个连续子序列，并在地形上放置k个瞭望塔，以便从同一个瞭望塔上可以看到子序列中的每个点位置，并且最小化瞭望塔的最大长度。我们针对这一问题的两个变体提出了有效的算法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.