Arithmetic interpolation search for alphabet tables

The inefficiency of interpolation search for an alphabetic table has been demonstrated by F.W. Burton and G.N. Lewis (1980). This inefficiency is expected since such tables are usually far from uniform in distribution. However, for nonuniformly distributed tables for which the cumulative distribution function F is known, applying F to the keys yields uniform distribution for which interpolation search is very fast. In arithmetic coding a string of characters is mapped into the (0, 1) interval according to the probabilities of its characters. It is found that this transformation, designed for data compression, is actually the cumulative distribution function F for alphabetic tables. Experiments confirm that interpolation search on alphabetic tables, applying arithmetic coding to the character strings in a sophisticated way, shows a performance very close to lg lg n accesses. Hence, a new fast search technique for alphabetic tables is designed.<
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