Box-trees and R-trees with near-optimal query time

Research output: Contribution to journalArticle


A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. The query complexity of a box-tree with respect to a given type of query is the maximum number of nodes visited when answering such a query. We describe several new algorithms for constructing box-trees with small worst-case query complexity with respect to queries with axis-parallel boxes and with points. We also prove lower bounds on the Worst-case query complexity for box-trees, which show that our results are optimal or close to optimal. Finally, we present algorithms to convert box-trees to R-trees, resulting in R-trees with (almost) optimal query complexity.


  • PK Agarwal
  • M de Berg
  • J Gudmundsson
  • Mikael Hammar
  • HJ Haverkort
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computer Science
Original languageEnglish
Pages (from-to)291-312
JournalDiscrete & Computational Geometry
Issue number3
Publication statusPublished - 2002
Publication categoryResearch