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Lecture No. 7, 10/8, Topics
Binary search trees with an additional tournament to represent priorities: supports queries
such as finding the maximum priority element in a given range, in O log n time per
query, insert, delete.
Priority search trees to handle 1-1/2 D range queries on 2D data.
E. McCreight, “Priority search trees,” SIAM J. Comput. 14 (1985), 257-276.
Interval trees and segment trees.
F. Preparata and M. Shamos, Computational Geometry: An Introduction, SpringerVerlag, 1985.
Dynamization
Add insertions to a static or deletions-only data structure by keeping data
partitioned into structures of exponentially increasing sizes, rebuilding structures
as insertions occur. Generally costs a log function in query and insertion time (if
rebuilding time is linear).
Related idea: in search trees, handle rotations via rebuilding, use weight-balanced
trees to obtain good amortized performance (logarithmic).
J. Bentley and J. Saxe, “Decomposable searching problems, I: static-to-dynamic
transformation,” J. Algorithms 1 (1980), 301-358.
J. Neivergelt and E. Reingold, “Binary search trees of bounded balance,” SIAM J.
Comput 2 (1973), 33-43.
K. Mehlhorn, Data Structures and Algorithms 1: Sorting and Searching, SpringerVerlag, 1984, 189-198.