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