A more cost effective algorithm for finding perfect hash functions

Abstract

of these contexts there are large static collections of records which must be indexed by keys, usually English words or phrases. Hashing is one method that can provide the desired rapid access, with little overhead in space, but unless the hash function chosen is suitable, there can be a considerable loss in performance due to collisions. Given adequate space, dynamic hashing methods have been developed to deal with this problem in changeable collections [ENBO88]. With static data sets, however, it is possible to build so-called "perfect" hash functions that require minimal space for the hash table, and which entirely avoid the problem of collisions.Electronic mail to: fox@vtopus.cs.vt.eduAs the use of knowledge-based systems increases, there will be a growing need for efficient artificial intelligence systems and methods to access large lexicons. In the COmposite Document Expert/extended/effective Retrieval (CODER) system we have, in order to provide rapid access to data items on CD-ROMs and to terms in a lexicon built from machine readable dictionaries, investigated the construction of perfect hash functions. We have considered algorithms reported earlier in the literature, have made numerous enhancements to them, have developed new algorithms, and here report on some of our results. This paper covers an O(n 3) algorithm that has been applied to building hash functions for a collection of 69806 words on a CD-ROM. Most recently we have developed a much better algorithm and have succeeded in finding a perfect hash function for a set of 130,199 words taken from sources including the Collins English Dictionary.

Finding succinct ordered minimal perfect hash functions

“…is of concern to us only insofar that good pseudo-random functions can be found which map the keys to integers. Several authors have given families of pseudo-random functions which work well for character string keys [4,5,6,7,10].…”

Using tries to eliminate pattern collisions in perfect hashing

“…2 would work well as a perfect hashing algorithm because it completely eliminates the pattem collision problem, and also because it produces minimal word lists that can be ordered in any way (the list shown is alphabetical). If the trie array were stored in memory, the CPU time needed to index a word through the hie would actually be less than that of other perfect hashing functions currently in use for handling large word sets [22], [9]. For example, to look up the word CORN using Sager's algorithm [22] (or Fox's improvement of it [9]) requires that seven characters be indexed from the word, along with 11 additions, three MOD operations, and three array indexings.…”

“…CD-ROM's also have slow track seek times, which makes multiple accesses to the disk extremely frustrating for the user of the CD-ROM. Perfect hashing functions have been used in this environment to provide quick access to large medical dictionaries [9] and other word lists. The perfect hashing function allows any word to be accessed from the disk with only one disk access operation.…”

Practical minimal perfect hash functions for large databases

“…After further investigation we developed a modified algorithm [16] requiring O(m 3) time. With this algorithm we were able to find MPHF's for sets of over a thousand words.…”

“…After careful analysis of Sager's algorithm [32] and our enhanced version [16], Heath made three crucial observations that serve as the foundation of our new algorithms:…”