Balanced aspect ratio trees: Combining the advantages of k-d trees and octrees

Christian A. Duncan, Michael T. Goodrich, Stephen Kobourov

Research output: Contribution to conferencePaperpeer-review

29 Scopus citations

Abstract

Given a set S of n points in Rd, we show, for fixed d, how to construct in O(n log n) time a data structure we call the Balanced Aspect Ratio (BAR) tree. A BAR tree is a binary space partition tree on S that has O(log n) depth and in which every region is convex and `fat' (that is, has a bounded aspect ratio). While previous hierarchical data structures, such as k-d trees, quadtrees, octrees, fair-split trees, and balanced box decompositions can guarantee some of these properties, we know of no previous data structure that combines all of these properties simultaneously. The BAR tree data structure has numerous applications ranging from solving several geometric searching problems in fixed dimensional space to aiding in the visualization of graphs and three-dimensional worlds.

Original languageEnglish (US)
Pages300-309
Number of pages10
StatePublished - 1999
Externally publishedYes
EventProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms - Baltimore, MD, USA
Duration: Jan 17 1999Jan 19 1999

Other

OtherProceedings of the 1999 10th Annual ACM-SIAM Symposium on Discrete Algorithms
CityBaltimore, MD, USA
Period1/17/991/19/99

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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