We consider static dictionaries over the universe U = on a unit-cost RAM with word size w. Construction of a static dictionary with linear space consumption and constant lookup time can be done in linear expected time by a randomized algorithm. In contrast, the best previous deterministic algorithm for constructing such a dictionary with n elements runs in time O(n ) for # > 0. This paper narrows the gap between deterministic and randomized algorithms exponentially, from the factor of to an O(log n) factor. The algorithm is weakly non-uniform, i.e. requires certain precomputed constants dependent on w. A by-product of the result is a lookup time vs insertion time trade-o# for dynamic dictionaries, which is optimal for a certain class of deterministic hashing schemes.

We consider dynamic dictionaries over the universe U = {0, 1}^w on a unit-cost RAM with word size w and a standard instruction set, and present a linear space deterministic dictionary accommodating membership queries in time (log log n)^O(1) and updates in time (log n)^O(1), where n is the size of the set stored. Previous solutions either had query time (log n) 18 or update time 2 !( p log n) in the worst case.

. We consider dictionaries over the universe U = f0; 1g w on a unit-cost RAM with word size w and a standard instruction set. We present a linear space deterministic dictionary with membership queries in time (log log n) O(1) and updates in time (log n) O(1) , where n is the size of the set stored. This is the rst such data structure to simultaneously achieve query time (log n) o(1) and update time O(2 (log n) c ) for a constant c < 1. 1 Introduction Among the most fundamental data structures is the dictionary. A dictionary stores a subset S of a universe U , oering membership queries of the form \x 2 S?". The result of a membership query is either 'no' or a piece of satellite data associated with x. Updates of the set are supported via insertion and deletion of single elements. Several performance measures are of interest for dictionaries: The amount of space used, the time needed to answer queries, and the time needed to perform updates. The most ecient dictionar...