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

  • Authors:

  • Pankaj K. Agarwal;Mark de Berg;Joachim Gudmundsson;Mikael Hammar;Herman J. Haverkort

  • Affiliations:

  • Center for Geometric Computing, Department of Computer Science, Box 90129 Duke University, Durham, NC;Institute of Information, and Computing Sciences, Utrecht University, PO Box 80089, 3508 TB Utrecht, The Netherlands;Institute of Information, and Computing Sciences, Utrecht University, POBox 80089, 3508 TB Utrecht, The Netherlands;Department of Computer Science, Lund University, Box 118, 221 00 Lund, Sweden;Institute of Information, and Computing Sciences, Utrecht University, PO Box 80089, 3508 TB Utrecht, The Netherlands

  • Venue:
  • SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
  • Year:
  • 2001

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Abstract

A box-tree is a \ifasci so-called \emph{bounding-volume hierarchy} \else bounding-volume hierarchy \fi 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.