, Volume 9, Issue 1, pp 23-29

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

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Summary

Given 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·N 1−1/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·N 1−1/k ) in both structures.

This author's research was supported in part by the National Science Foundation under grant MCS-76-17321 and in part by the Joint Service Electronics Program under contract DAAB-07-72-C-0259