Complexity Analysis of 2D KD-Tree Construction, Query and Modification Based on Master Theorem and Ptential Energy Analysis

XJTU 2024 CSUC Submission5 Authors

30 Mar 2024 (modified: 03 Apr 2024)XJTU 2024 CSUC SubmissionEveryoneRevisionsBibTeXCC BY 4.0
Keywords: Master theorem, KD-Tree, Amortized Analysis, Potential method
Abstract: With the increasing popularity of machine learning today, high-dimensional space retrieval has become an extremely important research direction, which has important applications in classification, clustering and database. Among them, KD-Tree is a very important and classical high-dimensional spatial retrieval data structure. This paper introduces the application of master theorem and potential energy analysis in the complexity analysis of 2D KD-Tree, discusses the complexity of KD-Tree construction, nearest neighbor query, deletion and insertion with rebuild, and focuses on the influence of dimension factors in the region query in 2D KD-Tree.
Submission Number: 5