Partial Match Queries in Two-Dimensional Quadtrees: a Probabilistic Approach

Nicolas Curien (1) , Adrien Joseph (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

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.

Mots clés: Quadtree; Partial match query; Fragmentation theory; Markov chain; Coupling; Integral equation

Domaines: Probabilités [math.PR]

Nicolas Curien, Adrien Joseph. Partial Match Queries in Two-Dimensional Quadtrees: a Probabilistic Approach. 2010. ⟨hal-00518352⟩