Balls and Bins: Smaller Hash Families and Faster Evaluation

A fundamental fact in the analysis of randomized algorithm is that when n balls are hashed into n bins independently and uniformly at random, with high probability each bin contains at most O(log n/ log log n) balls. In various applications, however, the assumption that a truly random hash function is available is not always valid, and explicit functions are required. In this paper we study the size of families (or, equivalently, the description length of their functions) that guarantee a maximal load of O(log n/ log log n) with high probability, as well as the evaluation time of their functions. Whereas such functions must be described using Ω(log n) bits, the best upper bound was formerly O(log2 n/ log log n) bits, which is attained by O(log n/ log log n)-wise independent functions. Traditional constructions of the latter offer an evaluation time of O(log n/ log log n), which according to Siegel’s lower bound [FOCS ’89] can be reduced only at the cost of significantly increa...

• Type: Journal
• Year: 2011
• Where: ECCC
• Authors: L. Elisa Celis, Omer Reingold, Gil Segev, Udi Wieder
• Keywords: ECCC 2011, ECommerce