Testing Performance (Time Analysis) of Nearest Neighbour (NN) Search Algorithms on K-d Trees

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Abstract

K-d tree (k-dimensional tree) is a space partitioning data structure for organizing points in a k-dimensional space. K-d tree, or Multidimensional Binary Search Tree is a useful data structure for several applications such as searches involving a multidimensional search key (e.g., Range Search and Nearest Neighbour Search). K-d trees are a special case of binary space partitioning trees.KNN Search is a searching algorithm with complexity O(N log N) {N= no. of data points}. This search algorithm is relatively better than brute force search {Complexity= O(n*k); where k=No. of neighbours searched, N=No. of Data Points in Kd tree} for dimensions N>>2D {N=No. of Points, D=Dimensionality of Tree}.Furthermore, Parallel KNN Search is much more efficient and performs better than KNN Search, as it harnesses parallel processing capabilities of computers and thus, results in better search time.This paper tests the time performance of KNN Search and Parallel KNN Search and compares them by plotting it on a 3D graph. A more comprehensive comparison is done by use of 2D graphs for each dimension(from 2 to 20).
K-d树上最近邻(NN)搜索算法的测试性能(时间分析
K-d树(k维树)是一种空间划分数据结构,用于组织k维空间中的点。K-d树,或多维二叉搜索树是一种有用的数据结构,适用于一些应用程序,如涉及多维搜索键的搜索(例如,范围搜索和最近邻搜索)。K-d树是二叉空间分区树的一种特殊情况。KNN Search是一种复杂度为O(N log N) {N= no的搜索算法。的数据点}。该搜索算法相对于蛮力搜索{复杂度= O(n*k);在k = No。被搜查的邻居,N=No。对于维数N>>2D {N=No。点,D=树的维数}。此外,并行KNN搜索比KNN搜索效率更高,性能更好,因为它利用了计算机的并行处理能力,因此可以获得更好的搜索时间。本文测试了KNN搜索和并行KNN搜索的时间性能,并在三维图上进行了比较。通过对每个维度(从2到20)使用2D图进行更全面的比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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