, Volume 62, Issue 1, pp 21–37

Biased Range Trees


DOI: 10.1007/s00453-010-9440-y

Cite this article as:
Dujmović, V., Howat, J. & Morin, P. Algorithmica (2012) 62: 21. doi:10.1007/s00453-010-9440-y


A data structure, called a biased range tree, is presented that preprocesses a set S of n points in ℝ2 and a query distribution D for 2-sided orthogonal range counting queries (a.k.a. dominance counting queries). The expected query time for this data structure, when queries are drawn according to D, matches, to within a constant factor, that of the optimal comparison tree for S and D. The memory and preprocessing requirements of the data structure are  O(nlog n).


Computational geometry Data structures Orthogonal range searching Distribution-sensitive data structures 

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada