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
On the Average Performance of Orthogonal Range Search in Multidimensional Data Structures
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Improving the performance of multidimensional search using fingers
Journal of Experimental Algorithmics (JEA)
ACM Transactions on Algorithms (TALG)
Partial match queries in random quadtrees
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Rank selection in multidimensional data
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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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 upper and lower bounds for the performance of range searches (Theorems 3 and 4) and a useful characterization of the cost of range search as a sum of the costs of partial match-like operations (Theorem 5). Using these results, we can get very precise asymptotic estimates for the expected cost of range searches (Theorem 6).