具有两个给定半径的圆的有界集合的k覆盖优化

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1515/comp-2020-0219

A. Khorkov, Sh. I. Galiev

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引用次数: 1

摘要

摘要提出了一种研究具有两个给定半径的圆的凸有界集的k-覆盖的数值方法。考虑了覆盖圆中心之间的距离受到约束的情况。描述了一种用于寻找这种圆的近似数量及其中心排列的算法。对于某些特定情况，找到了给定域的k覆盖密度的近似下界。我们使用0–1线性规划或一般整数线性规划模型。数值结果表明了所提方法的有效性。

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Optimization of a k-covering of a bounded set with circles of two given radii

Abstract A numerical method for investigating k-coverings of a convex bounded set with circles of two given radii is proposed. Cases with constraints on the distances between the covering circle centers are considered. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. We use either 0–1 linear programming or general integer linear programming models. Numerical results demonstrating the effectiveness of the proposed methods are presented.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.