The edge labeling of higher order Voronoi diagrams

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-05-21 DOI:10.1007/s10898-024-01386-0

Mercè Claverol, Andrea de las Heras Parrilla, Clemens Huemer, Alejandra Martínez-Moraian

引用次数: 0

Abstract

We present an edge labeling of order-k Voronoi diagrams, \(V_k(S)\), of point sets S in the plane, and study properties of the regions defined by them. Among them, we show that \(V_k(S)\) has a small orientable cycle and path double cover, and we identify configurations that cannot appear in \(V_k(S)\) for small values of k. This paper also contains a systematic study of well-known and new properties of \(V_k(S)\), all whose proofs only rely on elementary geometric arguments in the plane. The maybe most comprehensive study of structural properties of \(V_k(S)\) was done by D.T. Lee (On k-nearest neighbor Voronoi diagrams in the plane) in 1982. Our work reviews and extends the list of properties of higher order Voronoi diagrams.

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高阶 Voronoi 图的边标注

我们提出了平面中点集 S 的阶 k Voronoi 图（\(V_k(S)\)）的边标签，并研究了由它们定义的区域的性质。其中，我们证明了\(V_k(S)\)有一个小的可定向循环和路径双覆盖，我们还确定了在k的小值下不能出现在\(V_k(S)\)中的构型。本文还系统地研究了\(V_k(S)\)众所周知的和新的性质，所有这些性质的证明都只依赖于平面中的基本几何论证。也许对 \(V_k(S)\) 的结构性质最全面的研究是由 D.T. Lee 在 1982 年完成的（On k-nearest neighbor Voronoi diagrams in the plane）。我们的研究回顾并扩展了高阶 Voronoi 图的属性列表。

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

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.