A branching process arising in dynamic hashing, trie searching and polynomial factorization
We obtain average value and distribution estimates for the height of a class of trees that occurs in various contexts in computer algorithms : in trie searching, as index in several dynamic schemes and as an underlying partition structure in polynomial factorization algorithms. In particular, results given here completely solve the problem of analyzing Extendible Hashing for which practical conclusions are given. The treatment relies on the saddle point method of complex analysis which is used here for extracting coefficients of a probability generating function, and on a particular technique that reveals periodic fluctuations in the behaviour of algorithms which are precisely quantified.
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