Balanced Aspect Ratio Trees

Combining the Advantages of k-d Trees and Octrees

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

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

Given a set S of n points on 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 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 geometric searching problems in fixed dimensional space to the visualization of graphs and three-dimensional worlds.

Original languageEnglish (US)
Pages (from-to)303-333
Number of pages31
JournalJournal of Algorithms
Volume38
Issue number1
DOIs
StatePublished - Jan 2001

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Octree
Aspect Ratio
Data structures
Aspect ratio
Data Structures
Binary Space Partition
Hierarchical Data
Oils and fats
Quadtree
Tree Structure
Hierarchical Structure
Visualization
Decomposition
Decompose
Three-dimensional
Graph in graph theory

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

Balanced Aspect Ratio Trees : Combining the Advantages of k-d Trees and Octrees. / Duncan, Christian A.; Goodrich, Michael T.; Kobourov, Stephen G.

In: Journal of Algorithms, Vol. 38, No. 1, 01.2001, p. 303-333.

Research output: Contribution to journalArticle

Duncan, Christian A. ; Goodrich, Michael T. ; Kobourov, Stephen G. / Balanced Aspect Ratio Trees : Combining the Advantages of k-d Trees and Octrees. In: Journal of Algorithms. 2001 ; Vol. 38, No. 1. pp. 303-333.
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