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

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·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. © 1977 Springer-Verlag.