矩形Delaunay三角剖分的紧密跨越比

IF 0.7 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Algorithmica Pub Date : 2025-04-16 DOI:10.1007/s00453-025-01308-w

André van Renssen, Yuan Sha, Yucheng Sun, Sampson Wong

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引用次数: 0

摘要

扳手构造是一个研究得很好的问题，德劳内三角剖分法是最流行的扳手之一。如果使用等边三角形、正方形或正六边形构造德劳内三角剖分，则已知紧边界。然而，所有其他形状仍然难以捉摸。在本文中，我们扩展了已知紧界的受限扳手类。我们证明了用长宽比为\(A\)的矩形构造的Delaunay三角形的生成比不超过\(\sqrt{2} \sqrt{1+A^2 + A\sqrt{A^2 + 1}}\)，它符合已知的下界。

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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The Tight Spanning Ratio of the Rectangle Delaunay Triangulation

Spanner construction is a well-studied problem and Delaunay triangulations are among the most popular spanners. Tight bounds are known if the Delaunay triangulation is constructed using an equilateral triangle, a square, or a regular hexagon. However, all other shapes have remained elusive. In this paper, we extend the restricted class of spanners for which tight bounds are known. We prove that Delaunay triangulations constructed using rectangles with aspect ratio \(A\) have spanning ratio at most \(\sqrt{2} \sqrt{1+A^2 + A\sqrt{A^2 + 1}}\), which matches the known lower bound.

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来源期刊

Algorithmica 工程技术-计算机：软件工程

CiteScore

2.80

自引率

9.10%

发文量

158

审稿时长

12 months

期刊介绍： Algorithmica is an international journal which publishes theoretical papers on algorithms that address problems arising in practical areas, and experimental papers of general appeal for practical importance or techniques. The development of algorithms is an integral part of computer science. The increasing complexity and scope of computer applications makes the design of efficient algorithms essential. Algorithmica covers algorithms in applied areas such as: VLSI, distributed computing, parallel processing, automated design, robotics, graphics, data base design, software tools, as well as algorithms in fundamental areas such as sorting, searching, data structures, computational geometry, and linear programming. In addition, the journal features two special sections: Application Experience, presenting findings obtained from applications of theoretical results to practical situations, and Problems, offering short papers presenting problems on selected topics of computer science.