Bottleneck matching in the plane

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-06-01 DOI:10.1016/j.comgeo.2023.101986

Matthew J. Katz , Micha Sharir

引用次数: 0

Abstract

We present a randomized algorithm that with high probability finds a bottleneck matching in a set of $n = 2 ℓ$ points in the plane. The algorithm's running time is $O (n^{ω / 2} \log n)$ , where $ω > 2$ is a constant such that any two $n \times n$ matrices can be multiplied in time $O (n^{ω})$ . The state of the art in fast matrix multiplication allows us to set $ω = 2.3728596$ .

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飞机上的瓶颈匹配

我们提出了一种随机算法，该算法在n=2的集合中以高概率找到瓶颈匹配ℓ 平面中的点。该算法的运行时间为O（nω/2log⁡n），其中ω>；2是一个常数，使得任意两个n×n矩阵可以在时间O（nω）上相乘。快速矩阵乘法的最新技术允许我们设置ω=2.3728596。

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

Computational Geometry-Theory and Applications 数学-数学

CiteScore

1.60

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Computational Geometry is a forum for research in theoretical and applied aspects of computational geometry. The journal publishes fundamental research in all areas of the subject, as well as disseminating information on the applications, techniques, and use of computational geometry. Computational Geometry publishes articles on the design and analysis of geometric algorithms. All aspects of computational geometry are covered, including the numerical, graph theoretical and combinatorial aspects. Also welcomed are computational geometry solutions to fundamental problems arising in computer graphics, pattern recognition, robotics, image processing, CAD-CAM, VLSI design and geographical information systems. Computational Geometry features a special section containing open problems and concise reports on implementations of computational geometry tools.