An Exponential Open Hashing Function Based on Dynamical Systems Theory

In this paper an eecient open addressing hash function called exponential hashing is developed using concepts from dynamical systems theory and number theory. A comparison of exponential hashing versus a widely-used double hash function is performed using an analysis based on Lya-punov exponents and entropy. Proofs of optimal table parameter choices are provided for a number of hash functions. We also demonstrate experimentally that exponential hashing nearly matches the performance of an optimal double hash function for uniform data distributions, and performs signiicantly better for nonuniform data distributions. We show that exponential hashing exhibits a higher integer Lyapunov exponent and entropy than double hashing for initial data probes, which ooers one explanation for its improved performance on nonuniform data distributions. 1. INTRODUCTION The hash table is a well-known data structure used to maintain dynamic dictionaries. A dynamic dictionary is deened as a collection of data items that can be accessed according to the following operations: