覆盖海量点集的单元盘覆盖算法实验

IF 0.4 4区计算机科学 Q4 MATHEMATICS

Computational Geometry-Theory and Applications Pub Date : 2023-02-01 DOI:10.1016/j.comgeo.2022.101925

Rachel Friederich, Anirban Ghosh, Matthew Graham, Brian Hicks, Ronald Shevchenko

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引用次数: 0

摘要

给定平面中的一组n个点，单元磁盘覆盖（UDC）问题要求计算覆盖这些点所需的最小单元磁盘数量，以及磁盘的位置。这个问题是NP难的，在过去的三十年里已经设计了几种近似算法。在本文中，我们对其中一些算法在海量点集上的实际性能进行了设计和实验比较。目标是研究哪些算法运行速度快，并在实践中给出良好的近似值。我们为UDC提出了一个简单的7近似算法，该算法在O（n）预期时间内运行，并使用O（s）额外空间，其中s表示生成的覆盖的大小。在我们的实验中，它被证明是最快的。我们还提出了两种启发式方法，以在不降低速度的情况下减少它生成的覆盖物的大小。据我们所知，这是第一项对UDC问题的算法进行实验比较的工作。对它们使用大量点集（数以百万计）的实验揭示了它们的实际用途。我们通过GitHub1分享工程算法，以便在几何优化领域进行更广泛的应用和未来的研究。

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Experiments with unit disk cover algorithms for covering massive pointsets

Given a set of n points in the plane, the Unit Disk Cover (UDC) problem asks to compute the minimum number of unit disks required to cover the points, along with a placement of the disks. The problem is NP-hard and several approximation algorithms have been designed over the last three decades. In this paper, we have engineered and experimentally compared practical performances of some of these algorithms on massive pointsets. The goal is to investigate which algorithms run fast and give good approximation in practice.

We present a simple 7-approximation algorithm for UDC that runs in $O (n)$ expected time and uses $O (s)$ extra space, where s denotes the size of the generated cover. In our experiments, it turned out to be the speediest of all. We also present two heuristics to reduce the sizes of covers generated by it without slowing it down by much.

To our knowledge, this is the first work that experimentally compares algorithms for the UDC problem. Experiments with them using massive pointsets (in the order of millions) throw light on their practical uses. We share the engineered algorithms via GitHub¹ for broader uses and future research in the domain of geometric optimization.

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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.