Maximum-width rainbow-bisecting empty annulus

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2024-03-06 DOI:10.1016/j.comgeo.2024.102088

Sang Won Bae , Sandip Banerjee , Arpita Baral , Priya Ranjan Sinha Mahapatra , Sang Duk Yoon

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引用次数: 0

Abstract

Given a set of n colored points with k colors in the plane, we study the problem of computing a maximum-width rainbow-bisecting empty annulus (of objects specifically axis-parallel square, axis-parallel rectangle and circle) problem. We call a region rainbow if it contains at least one point of each color. The maximum-width rainbow-bisecting empty annulus problem asks to find an annulus A of a particular shape with maximum possible width such that A does not contain any input points and it bisects the input point set into two parts, each of which is a rainbow. We compute a maximum-width rainbow-bisecting empty axis-parallel square, axis-parallel rectangular and circular annulus in $O (n^{3})$ time using $O (n)$ space, in $O (k^{2} n^{2} \log n)$ time using $O (n \log n)$ space and in $O (n^{3})$ time using $O (n^{2})$ space respectively.

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最大宽度彩虹分光空环

给定平面上 k 种颜色的 n 个彩色点的集合，我们研究的是计算最大宽度彩虹等分线空环面（对象具体为轴平行的正方形、轴平行的矩形和圆形）问题。如果一个区域至少包含每种颜色的一个点，我们就称该区域为彩虹区域。最大宽度彩虹分叉空环问题要求找到一个特定形状的最大宽度环 A，使得 A 不包含任何输入点，并且将输入点集一分为二，每一部分都是彩虹。我们使用 O(n) 空间在 O(n3) 时间内、使用 O(nlogn) 空间在 O(k2n2logn) 时间内以及使用 O(n2) 空间在 O(n3) 时间内分别计算出了最大宽度的彩虹分叉空轴平行正方形、轴平行矩形和圆形环面。

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.