An efficient algorithm for identifying rainbow ortho-convex 4-sets in k-colored point sets

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, INFORMATION SYSTEMS

Information Processing Letters Pub Date : 2024-12-10 DOI:10.1016/j.ipl.2024.106551

David Flores-Peñaloza , Mario A. Lopez , Nestaly Marín , David Orden

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引用次数: 0

Abstract

Let P be a k-colored set of n points in the plane,

4 \leq k \leq n

. We study the problem of deciding if P contains a subset of four points of different colors such that its Rectilinear Convex Hull has positive area. We show this problem to be equivalent to deciding if there exists a point c in the plane such that each of the open quadrants defined by c contains a point of P, each of them having a different color. We provide an

O (n \log n)

-time algorithm for this problem, where the hidden constant does not depend on k; then, we prove that this problem has time complexity

Ω (n \log n)

in the algebraic computation tree model. No general position assumptions for P are required.

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k色点集中彩虹正凸4集的一种高效识别算法

设P为平面上n个点的k色集合，4≤k≤n。我们研究了判定P是否包含四个不同颜色的点的子集，使得它的直线凸包具有正的面积的问题。我们证明这个问题等价于判定平面上是否存在一个点c，使得每个由c定义的开放象限都包含一个点P，每个点都有不同的颜色。我们为这个问题提供了一个O（nlog (n)）时间算法，其中隐藏常数不依赖于k；然后，我们在代数计算树模型中证明了该问题具有时间复杂度Ω（nlog ln n）。不需要P的一般位置假设。

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

Information Processing Letters 工程技术-计算机：信息系统

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

7.3 months

期刊介绍： Information Processing Letters invites submission of original research articles that focus on fundamental aspects of information processing and computing. This naturally includes work in the broadly understood field of theoretical computer science; although papers in all areas of scientific inquiry will be given consideration, provided that they describe research contributions credibly motivated by applications to computing and involve rigorous methodology. High quality experimental papers that address topics of sufficiently broad interest may also be considered. Since its inception in 1971, Information Processing Letters has served as a forum for timely dissemination of short, concise and focused research contributions. Continuing with this tradition, and to expedite the reviewing process, manuscripts are generally limited in length to nine pages when they appear in print.