# Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees

@article{Lee2004WorstcaseAF,
title={Worst-case analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees},
author={D. T. Lee and Chak-Kuen Wong},
journal={Acta Informatica},
year={2004},
volume={9},
pages={23-29}
}
• Published 1 March 1977
• Computer Science
• Acta Informatica
SummaryGiven a file of N records each of which has k keys, the worst-case analysis for the region and partial region queries in multidimensional binary search trees and balanced quad trees are presented. It is shown that the search algorithms proposed in [1, 3] run in time O(k·N1−1/k) for region queries in both tree structures. For partial region queries with s keys specified, the search algorithms run at most in time O(s·N1−1/k) in both structures.
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