Uniform Hashing Is Optimal

Andrew Chi-Chih Yao

Abstract: It was conjectured by J. Ullman that uniform hashing is optimal in its expected retrieval cost among all open-address hashing schemes [4]. In this paper, we show that, for any open-address hashing scheme, the expected cost of retrieving a record from a large table that is α-fraction full is at least (1/α) log (1/(1 - α)) + o(1). This proves Ullman's conjecture to be true in the asymptotic sense.