A real elementary approach to the master recurrence and generalizations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationTheory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings
Pages14-26
Number of pages13
Volume6648 LNCS
DOIs
StatePublished - 2011
Event8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011 - Tokyo, Japan
Duration: May 23 2011May 25 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6648 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011
CountryJapan
CityTokyo
Period5/23/115/25/11

Fingerprint

Recurrence
Divide and conquer
Theorem
Simplicity
Proof by induction
Logarithmic
Generalization
Integer
Class

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Yap, C. (2011). A real elementary approach to the master recurrence and generalizations. In Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings (Vol. 6648 LNCS, pp. 14-26). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6648 LNCS). https://doi.org/10.1007/978-3-642-20877-5_3

A real elementary approach to the master recurrence and generalizations. / Yap, Chee.

Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings. Vol. 6648 LNCS 2011. p. 14-26 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6648 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Yap, C 2011, A real elementary approach to the master recurrence and generalizations. in Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings. vol. 6648 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6648 LNCS, pp. 14-26, 8th Annual Conference on Theory and Applications of Models of Computation, TAMC 2011, Tokyo, Japan, 5/23/11. https://doi.org/10.1007/978-3-642-20877-5_3
Yap C. A real elementary approach to the master recurrence and generalizations. In Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings. Vol. 6648 LNCS. 2011. p. 14-26. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-20877-5_3
Yap, Chee. / A real elementary approach to the master recurrence and generalizations. Theory and Applications of Models of Computation - 8th Annual Conference, TAMC 2011, Proceedings. Vol. 6648 LNCS 2011. pp. 14-26 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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