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

An ordered minimal perfect hash table is one in which no collisions occur among a predefined set of keys, no space is unused and the data are placed in the table in order. A new method for creating ordered minimal perfect hash functions is presented. It creates hash functions with representation space requirements closer to the theoretical lower bound than previous methods. The method presented requires approximately 17% less space to represent generated hash functions and is easy to implement. However, a high time complexity makes it practical for small sets only (size ! 1000). Keywords: Data Structures, Hashing, Perfect Hashing 1 Introduction A hash table is a data structure in which a number of keyed items are stored. To access an item with a given key, a hash function is used. The hash function maps from the set of keys, to the set of locations of the table. If more than one key maps to a given location, a collision occurs, and some collision resolution policy must be followed. O...