Balls Hierarchy: A Proximity Query for Metric Spaces and Covering Theorem

S. Kockara
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引用次数: 1

Abstract

In recent years, considerable advances have been made in the field of storing and processing moving data points. Data structures that discretely update moving objects or points are called Kinetic Data Structures. A particular type of data structure that constructs geometric spanner for moving point sets is called Deformable Spanner. This paper explores the underlying philosophy of deformable spanner and describes its rudiments. Deformable Spanners create a multi-resolution hierarchical subgraph that reflects a great deal about the original graph while maintaining all the existing proximity information in the graph. This proximity information plays a crucial role in wide variety of application areas, such as fast similarity queries in metric spaces, clustering in both dynamic and static multidimensional data, and cartographic representation of the complex networks. The motivation behind our work is twofold: first, to provide comprehensive understanding of the deformable spanner with sample illustrations without sacrificing depth of coverage; second, to analyze and improve deformable spanner’s covering property for 2D case in Euclidean space.
球层次:度量空间的邻近查询及覆盖定理
近年来,在存储和处理移动数据点方面取得了相当大的进展。离散地更新移动对象或点的数据结构称为动态数据结构。为移动点集构造几何扳手的一种特殊类型的数据结构称为可变形扳手。本文探讨了可变形扳手的基本原理,并介绍了其基本原理。可变形扳手创建一个多分辨率分层子图,该子图在保留图中所有现有接近信息的同时,反映了原始图的大量信息。这种接近信息在广泛的应用领域中起着至关重要的作用,例如度量空间中的快速相似性查询,动态和静态多维数据中的聚类以及复杂网络的制图表示。我们工作背后的动机是双重的:首先,在不牺牲覆盖深度的情况下,提供对示例插图的可变形扳手的全面了解;其次,分析并改进了二维欧几里德空间下变形扳手的覆盖特性。
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