Low redundancy in static dictionaries with O(1) worst case lookup time

Abstract

A static dictionary is a data structure for storing subsets of a finite universe U, so that membership queries can be answered efi- ciently. We study this problem in a unit cost RAM model with word size Ω (log /U/), and show that for n-element subsets, constant worst case query time can be obtained using B + O(log log /U/) + o(n) bits of sto- rage, where B = [log2(/U n/)] is the minimum number of bits needed to represent all such subsets. For /U/ = n logO(1) n the dictionary supports constant time rank queries. © Springer-Verlag Berlin Heidelberg 1999.