凸多边形上的分散问题

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

Information Processing Letters Pub Date : 2024-04-30 DOI:10.1016/j.ipl.2024.106498

Pawan K. Mishra , S.V. Rao , Gautam K. Das

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引用次数: 0

摘要

给定 R2 中 n 个点的集合 P={p1,p2,...,pn}和一个正整数 k (≤n)，我们希望找到 P 的大小为 k 的子集 S，使得子集 S 的代价 cost(S)=min{d(p,q)|p,q∈S} 最大，其中 d(p,q) 是两点 p 和 q 之间的欧氏距离。在本文中，我们考虑的是最大最小 k 分散问题，其中给定的 n 个点的集合 P 是一个凸多边形的顶点。我们把这个问题的变体称为凸 k-分散问题。我们为凸 k-分散问题提出了一种 1.733 因子近似算法。此外，我们还研究了 k=4 的凸 k-分散问题。我们提出了一种迭代算法，能在 O(n3) 时间内返回大小为 4 的最优解。

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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Dispersion problem on a convex polygon

Given a set $P = {p_{1}, p_{2}, \dots, p_{n}}$ of n points in $R^{2}$ and a positive integer k $(\leq n)$ , we wish to find a subset S of P of size k such that the cost of a subset S, $c o s t (S) = \min {d (p, q) | p, q \in S}$ , is maximized, where $d (p, q)$ is the Euclidean distance between two points p and q. The problem is called the max-min k-dispersion problem. In this article, we consider the max-min k-dispersion problem, where a given set P of n points are vertices of a convex polygon. We refer to this variant of the problem as the convex k-dispersion problem.

We propose an 1.733-factor approximation algorithm for the convex k-dispersion problem. In addition, we study the convex k-dispersion problem for $k = 4$ . We propose an iterative algorithm that returns an optimal solution of size 4 in $O (n^{3})$ time.

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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.