Abstract

Universal hash functions that exhibit c log n-wise independence are shown to give a performance in double hashing and virtually any reasonable generalization of double hashing that has an expected probe count of 1/(1-alpha) + epsilon for the insertion of the alpha n-th item into a table of size n, for any fixed alpha 0. This performance is within epsilon of optimal. These results are derived from a novel formulation that overestimates the expected probe count by underestimating the presence of partial items already inserted into the hash table, and from a sharp analysis of the underlying stochastic structures formed by colliding items.

Citations