Order preserving minimal perfect hash functions and information retrieval

Rapid access to information is essential for a wide variety of retrieval systems and applications. Hashing has long been used when the fastest possible direct search is desired, but is generally not appropriate when sequential or range searches are also required. This paper describes a hashing method, developed for collections that are relatively static, that supports both direct and sequential access. Indeed, the algorithm described gives hash functions that are optimal in terms of time and hash table space utilization, and that preserve any a priori ordering desired. Furthermore, the resulting order preserving minimal perfect hash functions (OPMPHFs) can be found using space and time that is on average linear in the number of keys involved.