一种简单随机O(n log n)时间最接近对加倍度量算法

Q4 Mathematics

International Journal of Computational Geometry & Applications Pub Date : 2020-04-13 DOI:10.20382/JOCG.V11I1A20

A. Maheshwari, Wolfgang Mulzer, M. Smid

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引用次数: 1

摘要

考虑一个度量空间$(P,dist)$，它有$N$个点，其倍维是一个常数。我们提出了一个简单的，随机的，递归的算法，在$O(N \log N)$期望时间内，计算$P$中最近的对距离。为了生成递归调用，我们使用先前的Har-Peled和Mendel的结果，以及Abam和Har-Peled的结果来计算以平衡方式分离点的稀疏环。

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A Simple Randomized O(n log n)-Time Closest-Pair Algorithm in Doubling Metrics

Consider a metric space $(P,dist)$ with $N$ points whose doubling dimension is a constant. We present a simple, randomized, and recursive algorithm that computes, in $O(N \log N)$ expected time, the closest-pair distance in $P$. To generate recursive calls, we use previous results of Har-Peled and Mendel, and Abam and Har-Peled for computing a sparse annulus that separates the points in a balanced way.

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来源期刊

International Journal of Computational Geometry & Applications 数学-计算机：理论方法

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The International Journal of Computational Geometry & Applications (IJCGA) is a quarterly journal devoted to the field of computational geometry within the framework of design and analysis of algorithms. Emphasis is placed on the computational aspects of geometric problems that arise in various fields of science and engineering including computer-aided geometry design (CAGD), computer graphics, constructive solid geometry (CSG), operations research, pattern recognition, robotics, solid modelling, VLSI routing/layout, and others. Research contributions ranging from theoretical results in algorithm design — sequential or parallel, probabilistic or randomized algorithms — to applications in the above-mentioned areas are welcome. Research findings or experiences in the implementations of geometric algorithms, such as numerical stability, and papers with a geometric flavour related to algorithms or the application areas of computational geometry are also welcome.