Generating Minimal Perfect Hash Functions

The randomized, deterministic and parallel algorithms for generating minimal perfect hash functions (MPHF) are proposed. Given a set of keys, W, which are character strings over some alphabet, the algorithms using a three-step approach (mapping, ordering, searching) nd the MPHF of the form h(w) = (h0(w) + g(h1(w)) + g(h2(w)))mod m, w 2 W, where h0, h1, h2 are auxiliary pseudorandom functions, m is a number of input keys, and g is a function implemented as a lookup table. The randomized and deterministic algorithms are time optimal, i.e. they construct the MPHF | of relatively large representation space | in expected time O(m). The time complexity of the parallel algorithm is exponential in m, but it generates the space eecient MPHF. The algorithm which is based on a specially devised data structure, called a reversed trie, exhibits a consistent and almost linear speedup in the number of processors on a message-based distributed-memory computer. The results of timing experiments conducted on the implementations of the algorithms are presented.