多边形曲线的分组性逼近

IF 0.4 4区 计算机科学 Q4 MATHEMATICS
Joachim Gudmundsson , Yuan Sha, Sampson Wong
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引用次数: 0

摘要

2012年,Driemel等人引入了c填充曲线的概念,将其作为一种现实的输入模型。在c为常数的情况下,他们给出了一种近似线性时间(1+ε)的算法来计算两条c填充多边形曲线之间的Fréchet距离。从那时起,许多论文都使用了该模型。在本文中,我们考虑计算Rd中给定的多边形曲线是c填充的最小c的问题。我们提出了两种近似算法。第一个算法是2-近似算法,在O(dn2log)中运行⁡n) 时间。在d=2的情况下,我们开发了一种更快的算法,该算法返回一个(6+ε)-近似值,并在O(((n/ε3)4/3对数(n/ε))时间内运行。我们还实现了第一种算法,并计算了16组真实世界轨迹的近似分组度值。实验表明,对于许多曲线和轨迹,c分组性概念是一个有用的现实输入模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximating the packedness of polygonal curves

In 2012 Driemel et al. introduced the concept of c-packed curves as a realistic input model. In the case when c is a constant they gave a near linear time (1+ε)-approximation algorithm for computing the Fréchet distance between two c-packed polygonal curves. Since then a number of papers have used the model.

In this paper we consider the problem of computing the smallest c for which a given polygonal curve in Rd is c-packed. We present two approximation algorithms. The first algorithm is a 2-approximation algorithm and runs in O(dn2logn) time. In the case d=2 we develop a faster algorithm that returns a (6+ε)-approximation and runs in O((n/ε3)4/3polylog(n/ε))) time.

We also implemented the first algorithm and computed the approximate packedness-value for 16 sets of real-world trajectories. The experiments indicate that the notion of c-packedness is a useful realistic input model for many curves and trajectories.

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来源期刊
CiteScore
1.60
自引率
16.70%
发文量
43
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.
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