Istituto di Scienza e Tecnologie dell'Informazione     
Sprugnoli R. Perfect hashing functions: a single probe retrieving method for static sets. In: Communications of the Acm, vol. 20 (11) pp. 841 - 850. ACM, 1977.
A refinement of hashing which allows retrieval of an item in a static table with a single probe is considered. Given a set I of identifiers, two methods are presented for building, in a mechanical way, perfect hashing functions, i.e. functions transforming the elements of I into unique addresses. The first method, the "quotient redution" method, is shown to be complete in the sense that for every set I the smallest table in which the elements of I can be stored and from which they can be retrieved by using a perfect hashing function constructed by this method can be found. However, for nonuniformly distributed sets, this method can give rather sparse table. the second method, the "remainder reduction" method, is not complete in the above sense, but it seems to give minimal (or almost minimal) table for every kind of set. The two techniques are applicable directly to small sets. Some methods to extend these results to larger sets are also presented. A rough comparison with ordinary hashing is given which shows that this method can be used conveniently in several practical applications.
Subject Hashing
Hashing methods
Hash coding
Direct addressing

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