Advances in Applied Probability

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

Nicolas Curien and Adrien Joseph

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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

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

First available in Project Euclid: 15 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Quadtree partial match query fragmentation theory Markov chain coupling integral equation


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.

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