Statistics on performance are presented, both in terms of time and in terms of maximum and total cosets defined for selected enumerations. A new algorithm for generating order preserving minimal perfect hash functions is presented. The algorithm is probabilistic, involving generation of random graphs. It uses expected linear time and requires a linear number words to represent the hash function, and thus is optimal up to constant factors. It runs very fast in practice.
Group theory is a particularly fertile field for the design of practical algorithms.
Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational group theory may be used to gain insight into the general structure of algebraic algorithms. This paper examines the basic ideas behind some of the more important algorithms for finitely presented groups and permutation groups, and surveys recent developments in these fields. We review previous methods for finding minimal perfect hash functions, showing that the earlier ones have no serious practical value for large sets. Then we present optimal time solutions to the problem, which generate minimal perfect hash functions for arbitrary sets in expected linear time and use almost linear space.