Analysis of kdt-trees: Kd-trees improved by local reorganisations

  • Walter Cunto
  • Gustavo Lau
  • Philippe Flajolet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 382)


This paper deals with kd-tree like structures that implement the multidimensional dictionary. It presents the first efficient online reorganisation method that improves the performance of kd-trees. We propose a new variation of kd-trees, to be called kdt-trees, whereby the updating procedures guarantee that any subtree of size greater than 2t, t≥0, has at least t nodes on each side. Thus, kd-trees are a special case of kdt-trees with t=0. The analysis developed provides, for the first time, an asymptotic expression for the variance of the performance of partial match queries in kd-tree like structures. The relevance of kdt-trees is supported by the fact that they approach the performance of fully balanced kd-trees for small values of t.


Search Pattern Lower Order Term Probability Generate Function Binary Search Tree Domain Dimension 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Walter Cunto
    • 1
  • Gustavo Lau
    • 2
  • Philippe Flajolet
    • 3
  1. 1.Centro Científico, IBM de VenezuelaCaracasVenezuela
  2. 2.Departamento de Matemáticas y Ciencias de la ComputaciónUniversidad Simón BolívarCaracasVenezuela
  3. 3.INRIALes Chesnay CedexFrance

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