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}
}
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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