Advances in Applied Probability

Partial match queries in two-dimensional quadtrees: a probabilistic approach

Nicolas Curien and Adrien Joseph

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Abstract

We analyze the mean cost of the partial match queries in random two-dimensional quadtrees. The method is based on fragmentation theory. The convergence is guaranteed by a coupling argument of Markov chains, whereas the value of the limit is computed as the fixed point of an integral equation.

Article information

Source
Adv. in Appl. Probab., Volume 43, Number 1 (2011), 178-194.

Dates
First available in Project Euclid: 15 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.aap/1300198518

Digital Object Identifier
doi:10.1239/aap/1300198518

Mathematical Reviews number (MathSciNet)
MR2761153

Zentralblatt MATH identifier
1215.68083

Subjects
Primary: 60F99: None of the above, but in this section
Secondary: 60G18: Self-similar processes 60J05: Discrete-time Markov processes on general state spaces

Keywords
Quadtree partial match query fragmentation theory Markov chain coupling integral equation

Citation

Curien, Nicolas; Joseph, Adrien. Partial match queries in two-dimensional quadtrees: a probabilistic approach. Adv. in Appl. Probab. 43 (2011), no. 1, 178--194. doi:10.1239/aap/1300198518. https://projecteuclid.org/euclid.aap/1300198518


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References

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