Summary: PREPRINT. In Proc. Symposium on Optimal Algorithms,
pages106114. Springer Verlag, 1989.
Optimal Bounds on the Dictionary Problem
Department of Computer Science
A new data structure for the dictionary problem is presented. Updates are per
formed in \Theta(log n) time in the worst case and the number of comparisons per op
eration is dlog n + 1 + ffle, where ffl is an arbitrary positive constant.
One of the fundamental and most studied problems in computer science is the dictionary
problem, that is the problem of how to maintain a set of data during the operations search,
insert and delete. It is well known that in a comparisonbased model the lower bound on
these operations is dlog(n + 1)e comparisons both in the average and in the worst case.
This bound can be achieved by storing the set in an array or in a perfectly balanced
binary search tree. However, for both these data structures the overhead cost per update
is high, \Theta(n) in the worst case.
An efficient dynamic data structure for the dictionary problem should have a worst case