A Simulated Annealing Algorithm for Generating Minimal Perfect Hash Functions

We developed minimal perfect hash functions for a variety of datasets using the probabilistic process of simulated annealing (SA). The SA solution structure is a tree representing an annealed program (algorithm). This solution structure is similar to the structure used in genetic programming. When executed, the SA program produces multiple hash functions for the given data set. An initial hash function called the distribution function is generated. This function attempts to uniformly place the keys into bins in preparation for a minimal perfect hash function determined later. For each trial, and for every data set of various size tested, our algorithm annealed a minimal perfect hash function. Our algorithm is applied to datasets of strings from the English language and to a list of URL’s. Bloat control is used to ensure a small fixed depth limit to our solution, to simplify function complexity, and to ensure fast evaluation. Experimental results show that our algorithm generates hash functions which outperform both widely known non-minimal, non-perfect hashing schemes as well as other recent algorithms from the literature. Keywords-Minimal Perfect Hash Functions; Differential Evolution; Simulated Annealing; Genetic Programming; Hashing