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. Keywords: Data structures, probabilistic algorithms, analysis of algorithms, hashing, random graphs

This paper describes a practical application of a novel terminal attractor algorithm to the construction of Perfect Hash Functions (PHF) for a predefined set of keys. The proposed method, which can be used in the ordering phase of a classical Mapping, Deterministic Ordering and Searching (MDOS) approach, is based on a neural network canonical form of efficient gradient descent, for solving linear systems, named ELISA. Numerical experiments clearly show that ELISA is able to determine the optimal solution in many difficult cases, where other alternative algorithms fail or are ineffective.