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

Part of: Markov processes Stochastic processes Limit theorems

Published online by Cambridge University Press:  01 July 2016

Nicolas Curien  and
Adrien Joseph
Nicolas Curien*
Affiliation:
École Normale Supérieure
Adrien Joseph*
Affiliation:
Université Pierre et Marie Curie
*
∗ Postal address: Département de Mathématiques et Applications, École Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France. Email address: [email protected]
∗∗ Postal address: Laboratoire de Probabilités et Modèles Aléatoires, Université Pierre et Marie Curie, 4 place Jussieu Tour 16-26, 75005 Paris, France. Email address: [email protected]
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Abstract

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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.

Keywords

Quadtreepartial match queryfragmentation theoryMarkov chaincouplingintegral equation

MSC classification

Primary: 60F99: None of the above, but in this section
Secondary: 60G18: Self-similar processes 60J05: Discrete-time Markov processes on general state spaces
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 1 , March 2011 , pp. 178 - 194
Copyright
Copyright © Applied Probability Trust 2011 

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