Analysis of range search for random k-d trees

被引：3
|
作者：
Philippe Chanzy
Luc Devroye
Carlos Zamora-Cura
机构：
[1] School of Computer Science,
[2] McGill University,undefined
[3] Montreal,undefined
[4] Canada H3A 2K6 (e-mail: {luc,undefined
[5] czamora}@cs.mcgill.ca),undefined
来源：
Acta Informatica | 2001年 / 37卷
关键词：
Time Complexity; Time Analysis; Probabilistic Method; Random Point; Neighbor Search;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We analyze the expected time complexity of range searching with k-d trees in all dimensions when the data points are uniformly distributed in the unit hypercube. The partial match results of Flajolet and Puech are reproved using elementary probabilistic methods. In addition, we give asymptotic expected time analysis for orthogonal and convex range search, as well as nearest neighbor search. We disprove a conjecture by Bentley that nearest neighbor search for a given random point in the k-d tree can be done in O(1) expected time.
引用
收藏
页码：355 / 383
页数：28
相关论文
共 50 条
  • [1] Analysis of range search for random k-d trees
    Chanzy, P
    Devroye, L
    Zamora-Cura, C
    ACTA INFORMATICA, 2001, 37 (4-5) : 355 - 383
  • [2] AVERAGE CASE ANALYSIS OF REGION SEARCH IN BALANCED K-D TREES
    SILVAFILHO, YV
    INFORMATION PROCESSING LETTERS, 1979, 8 (05) : 219 - 223
  • [3] Partial match queries in random k-d trees
    Chern, HH
    Hwang, HK
    SIAM JOURNAL ON COMPUTING, 2006, 35 (06) : 1440 - 1466
  • [4] On the average cost of insertions on random relaxed K-d trees
    Duch, Amalia
    Martinez, Comado
    PROCEEDINGS OF THE NINTH WORKSHOP ON ALGORITHM ENGINEERING AND EXPERIMENTS AND THE FOURTH WORKSHOP ON ANALYTIC ALGORITHMICS AND COMBINATORICS, 2007, : 194 - 200
  • [5] DIVIDED K-D TREES
    VANKREVELD, MJ
    OVERMARS, MH
    ALGORITHMICA, 1991, 6 (06) : 840 - 858
  • [6] Orthogonal Range Searching in Moderate Dimensions: k-d Trees and Range Trees Strike Back
    Chan, Timothy M.
    DISCRETE & COMPUTATIONAL GEOMETRY, 2019, 61 (04) : 899 - 922
  • [7] Orthogonal Range Searching in Moderate Dimensions: k-d Trees and Range Trees Strike Back
    Timothy M. Chan
    Discrete & Computational Geometry, 2019, 61 : 899 - 922
  • [8] Squarish k-d trees
    Devroye, L
    Jabbour, J
    Zamora-Cura, C
    SIAM JOURNAL ON COMPUTING, 2000, 30 (05) : 1678 - 1700
  • [9] Traffic Sign Classification using K-d trees and Random Forests
    Zaklouta, Fatin
    Stanciulescu, Bogdan
    Hamdoun, Omar
    2011 INTERNATIONAL JOINT CONFERENCE ON NEURAL NETWORKS (IJCNN), 2011, : 2151 - 2155
  • [10] Fast Search Using k-d Trees with Fine Search for Spectral Data Identification
    Son, Youngjae
    Chen, Tiejun
    Baek, Sung-June
    MATHEMATICS, 2025, 13 (04)
12345