A real elementary approach to the master recurrence and generalizations

Authors:
Chee Yap
Affiliations:
Courant Institute of Mathematical Sciences, New York University, New York, NY and Korea Institute of Advanced Study, Seoul, Korea
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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Abstract

The master theorem provides a solution to a well-known divide-and-conquer recurrence, called here the master recurrence. This paper proves two cook-book style generalizations of this master theorem. The first extends the treated class of driving functions to the natural class of exponential-logarithmic (EL) functions. The second extends the result to the multiterm master recurrence. The power and simplicity of our approach comes from re-interpreting integer recurrences as real recurrences, with emphasis on elementary techniques and real induction.