Partial match retrieval of multidimensional data
Journal of the ACM (JACM)
Finite element mesh generation methods: a review and classification
Computer-Aided Design
Applications of spatial data structures: Computer graphics, image processing, and GIS
Applications of spatial data structures: Computer graphics, image processing, and GIS
The design and analysis of spatial data structures
The design and analysis of spatial data structures
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Asymptotic distributions for partial match queries in K-d trees
Proceedings of the ninth international conference on on Random structures and algorithms
Multidimensional binary search trees used for associative searching
Communications of the ACM
On a multivariate contraction method for random recursive structures with applications to Quicksort
Random Structures & Algorithms - Special issue on analysis of algorithms dedicated to Don Knuth on the occasion of his (100)8th birthday
On the average performance of orthogonal range search in multidimensional data structures
Journal of Algorithms - Analysis of algorithms
Randomized K-Dimensional Binary Search Trees
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Foundations of Multidimensional and Metric Data Structures (The Morgan Kaufmann Series in Computer Graphics and Geometric Modeling)
A Modified Quadtree Approach To Finite Element Mesh Generation
IEEE Computer Graphics and Applications
Analytic Combinatorics
Hypergeometrics and the cost structure of quadtrees
Random Structures & Algorithms
Rank selection in multidimensional data
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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We consider the problem of recovering items matching a partially specified pattern in multidimensional trees (quad trees and k-d trees). We assume the traditional model where the data consist of independent and uniform points in the unit square. For this model, in a structure on n points, it is known that the number of nodes Cn (ζ) to visit in order to report the items matching an independent and uniformly on [0, 1] random query ζ satisfies E[Cn(ζ)] ~ κnβ, where κ and β are explicit constants. We develop an approach based on the analysis of the cost Cn(x) of any fixed query x ε [0, 1], and give precise estimates for the variance and limit distribution of the cost Cn(x). Our results permit to describe a limit process for the costs Cn(x) as x varies in [0, 1]; one of the consequences is that E[maxxε[0, 1] Cn(x)] ~ γnβ; this settles a question of Devroye [Pers. Comm., 2000].