论文标题
一种实用算法来计算帽差异
A practical algorithm to calculate Cap Discrepancy
论文作者
论文摘要
研究人员很长一段时间以来一直在研究这些观点，并在数学和计算机科学的不同领域中应用。评估给定分布均匀性的众所周知的措施之一是差异，它评估了通过将质量点放在给定集合点的统一分布与经验分布之间的差异。尽管差异对于衡量统一性非常有用，但准确计算在计算上具有挑战性。我们介绍了基于我们开发出一种称为定向差异的算法的定向差异的概念，该算法可以为在单位球体上分布在单位球体上的有限集的上限差异提供准确的近似，$ \ mathbb {s}^^2。并实际上通过计算特定分布（极性坐标）的盖限量来评估其容量，该分布的额极坐标旨在在球体上均匀分布点。
Uniform distribution of the points has been of interest to researchers for a long time and has applications in different areas of Mathematics and Computer Science. One of the well-known measures to evaluate the uniformity of a given distribution is Discrepancy, which assesses the difference between the Uniform distribution and the empirical distribution given by putting mass points at the points of the given set. While Discrepancy is very useful to measure uniformity, it is computationally challenging to be calculated accurately. We introduce the concept of directed Discrepancy based on which we have developed an algorithm, called Directional Discrepancy, that can offer accurate approximation for the cap Discrepancy of a finite set distributed on the unit Sphere, $\mathbb{S}^2.$ We also analyze the time complexity of the Directional Discrepancy algorithm precisely; and practically evaluate its capacity by calculating the Cap Discrepancy of a specific distribution, Polar Coordinates, which aims to distribute points uniformly on the Sphere.
