Partial match retrieval of multidimensional data
Journal of the ACM (JACM)
The design and analysis of spatial data structures
The design and analysis of spatial data structures
Data Structures for Range Searching
ACM Computing Surveys (CSUR)
Multidimensional binary search trees used for associative searching
Communications of the ACM
Analysis of range search for random k-d trees
Acta Informatica
SIAM Journal on Computing
Analysis of KDT-Trees: KD-Trees Improved by Local Reogranisations
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
Randomized K-Dimensional Binary Search Trees
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
On the average performance of orthogonal range search in multidimensional data structures
Journal of Algorithms - Analysis of algorithms
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In this work we present the average-case analysis of orthogonal range search for several multidimensional data structures. We first consider random relaxed K-d trees as a prototypical example. Later we extend these results to many different multidimensional data structures. We show that the performance of range searches is related to the performance of a variant of partial matches using a mixture of geometric and combinatorial arguments. This reduction simplifies the analysis and allows us to give exact lower and upper bounds for the performance of range searches. Furthermore, under suitable conditions ("small range queries"), we can also get a very precise asymptotic estimate for the expected cost of range searches.