Practical perfect hashing in nearly optimal space

摘要

A hash function is a mapping from a key universe U to a range of integers, i.e.,h : U_→ {0,1.....m-1}, where m is the range's size. A perfect hash function for some set S is contained in U is a hash function that is one-to-one on S, where m ≥ ∣S∣. A minimal perfect hash function for some set S?U is a perfect hash function with a range of minimum size, i.e., m = ∣S∣. This paper presents a construction for (minimal) perfect hash functions that combines theoretical analysis, practical performance, expected linear construction time and nearly optimal space consumption for the data structure. For n keys and m=n the space consumption ranges from 2.62n + o(n) to 3.3n+o(n) bits, and for m = 1.23n it ranges from 1.95n + o(n) to 2.7n+o(n) bits. This is within a small constant factor from the theoretical lower bounds of 1.44n bits for m=n and 0.89n bits for m = 1.23n. We combine several theoretical results into a practical solution that has turned perfect hashing into a very compact data structure to solve the membership problem when the key set S is static and known in advance. By taking into account the memory hierarchy we can construct (minimal) perfect hash functions for over a billion keys in 46 min using a commodity PC. An open source implementation of the algorithms is available at under the GNU Lesser General Public License (LGPL).