Practical perfect hashing in nearly optimal space

A hash function is a mapping from a key universe U to a range of integers, i.e., image, where m is the rangeʹs size. A perfect hash function for some set image is a hash function that is one-to-one on S, where image. A minimal perfect hash function for some set image is a perfect hash function with a range of minimum size, i.e., image. 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 image to image bits, and for image it ranges from image to image bits. This is within a small constant factor from the theoretical lower bounds of image bits for m=n and image bits for image. 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).