Piercing pairwise intersecting geodesic disks by five points

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-02-01 DOI:10.1016/j.comgeo.2022.101947

A. Karim Abu-Affash , Paz Carmi , Meytal Maman

引用次数: 0

Abstract

Given a simple polygon P on n vertices and a set $D$ of m pairwise intersecting geodesic disks in P, we show that five points in P are always sufficient to pierce all the disks in $D$ . The points can be computed in $O ((n + m) \log n_{r})$ time, where $n_{r}$ is the number of the reflex vertices of P. This improves the previous bound of 14, obtained by Bose, Carmi, and Shermer [1].

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用五点刺穿成对相交的测地圆盘

给定n个顶点上的一个简单多边形P和P中m个成对相交的测地圆盘的集合D，我们证明了P中的五个点总是足以穿透D中的所有圆盘⁡nr）时间，其中nr是P的反射顶点的数量。这改进了Bose、Carmi和Shermer[1]获得的14的先前界。

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.