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A Real Elementary Approach to the Master Recurrence and Generalizations

  • Conference paper
Theory and Applications of Models of Computation (TAMC 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6648))

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.

This work is supported by an National Science Foundation Grants #CCF-0728977 and #CCF-0917093, and also with KIAS support.

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Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, New York University, New York, NY, 10012, USA

    Chee Yap

  2. Korea Institute of Advanced Study, Seoul, Korea

    Chee Yap

Authors
  1. Chee Yap
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Miami, 1365 Memorial Drive, 33146, Coral Gables, FL, USA

    Mitsunori Ogihara

  2. Department of Information and Communication Engineering, University of Electro-Comm, Chofugaoga 1-5-1, Chofu, 182-8585, Tokyo, Japan

    Jun Tarui

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Yap, C. (2011). A Real Elementary Approach to the Master Recurrence and Generalizations. In: Ogihara, M., Tarui, J. (eds) Theory and Applications of Models of Computation. TAMC 2011. Lecture Notes in Computer Science, vol 6648. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20877-5_3

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  • DOI: https://doi.org/10.1007/978-3-642-20877-5_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20876-8

  • Online ISBN: 978-3-642-20877-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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