ON RAMANUJAN'S Q{FUNCTIONy
نویسندگان
چکیده
This study provides a detailed analysis of a function which Knuth discovered to play a central r^ ole in the analysis of hashing with linear probing. The function, named after Knuth Q(n), is related to several of Ramanujan's investigations. It surfaces in the analysis of a variety of algorithms and discrete probability problems including hashing, the birthday paradox, random mapping statistics, the \rho" method for integer factorization, union{{nd algorithms, optimum caching, and the study of memory connicts. A process related to the complex asymptotic methods of singularity analysis and saddle point integrals permits to precisely quantify the behaviour of the Q(n) function. In this way, tight bounds are derived.
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تاریخ انتشار 1992