Piercing unit geodesic disks

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2025-06-16 DOI:10.1016/j.comgeo.2025.102209

Ahmad Biniaz , Prosenjit Bose , Thomas Shermer

引用次数: 0

Abstract

We prove that at most 3 points are always sufficient to pierce a set of m pairwise intersecting unit geodesic disks inside a simple polygon P with n vertices of which

n_{r}

are reflex. We provide an

O (n + m \log n_{r})

-time algorithm to compute these at most 3 piercing points. Our bound is tight since it is known that in certain cases 3 points are necessary.

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穿透单元测地线盘

证明了在具有n个反射顶点的简单多边形P内，至多3个点总是足以刺穿m组成对相交的单位测地圆盘。我们提供了一个O（n+mlog (nr)）时间算法来计算最多3个穿孔点。我们的界限很紧，因为已知在某些情况下需要3个点。

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.