Limit laws for partial match queries in quadtrees

Limit laws for partial match queries in quadtrees

Ralph Neininger and Ludger Rüschendorf

Source: Ann. Appl. Probab. Volume 11, Number 2 (2001), 452-469.

Abstract

It is proved that in an idealized uniform probabilistic model the cost of a partial match query in a multidimensional quadtree after normalization converges in distribution. The limiting distribution is given as a fixed point of a random affine operator. Also a first-order asymptotic expansion for the variance of the cost is derived and results on exponential moments are given. The analysis is based on the contraction method.

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Primary Subjects: 68Q25, 60F05

Secondary Subjects: 68P10

Keywords: Quadtree; partial match query; contraction method; multidimensional data structure; analysis of algorithms

Full-text: Open access

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aoap/1015345300
Mathematical Reviews number (MathSciNet): MR1843054
Digital Object Identifier: doi:10.1214/aoap/1015345300
Zentralblatt MATH identifier: 1012.68058

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