Faster deterministic dictionaries

We consider static dictionaries over the universe U = {0, 1}(w) 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(1+epsilon)) for epsilon > O. This paper narrows the gap between deterministic and randomized algorithms exponentially, from the factor of n(epsilon) 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-off for dynamic dictionaries, which is optimal for a realistic class of deterministic hashing schemes.