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International Colloquium on Automata, Languages, and Programming

ICALP 1997: Automata, Languages and Programming pp 449–459Cite as

An improved master theorem for divide-and-conquer recurrences

  • Session 11: Analysis of Algorithms
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1256))

Abstract

We present a new master theorem for the study of divide-and-conquer recursive definitions, which improves the old one in several aspects. In particular, it provides more information, frees us completely from technicalities like floors and ceilings, and covers a wider set of toll functions and weight distributions, stochastic recurrences included.

This research was supported by the ESPRIT LTR Project ALCOM-IT, contract # 20244 and by a grant from CIRIT (Comissió Interdépartamental de Recerca i Innovació Tecnològica).

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References

  1. T.H. Cormen, C.E. Leiserson, and R.L. Rivest. Introduction to Algorithms. The MIT Press, Cambridge, MA, 1990.

    Google Scholar 

  2. Philippe Flajolet, Gaston Gonnet, Claude Puech, and J.M. Robson. Analytic variations on quadtrees. Algorithmica, 10:473–500, 1993.

    Article  Google Scholar 

  3. C. A. R. Hoare. Find (Algorithm 65). Communications of the ACM, 4:321–322, 1961.

    Article  Google Scholar 

  4. C. A. R. Hoare. Quicksort. Computer Journal, 5:10–15, 1962.

    Article  Google Scholar 

  5. Robert Sedgewick and Philippe Flajolet. An Introduction to the Analysis of Algorithms. Addison-Wesley, 1996.

    Google Scholar 

  6. M.H. van Emden. Increasing the efficiency of quicksort. Communications of the ACM, 13:563–567, 1970.

    Article  Google Scholar 

  7. Rakesh M. Verma. A general method and a master theorem for divide-and-conquer recurrences with applications. Journal of Algorithms, 16:67–79, 1994.

    Article  Google Scholar 

  8. Rakesh M. Verma. General techniques for analyzing recursive algorithms with applications. SIAM Journal on Computing, 26(2):568–581, 1997.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Departament de Llenguatges i Sistemes Informàtics, Universitat Politècnica de Catalunya, E-08028, Barcelona, Catalonia, Spain

    Salvador Roura

Authors
  1. Salvador Roura
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Editor information

Pierpaolo Degano Roberto Gorrieri Alberto Marchetti-Spaccamela

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© 1997 Springer-Verlag Berlin Heidelberg

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Roura, S. (1997). An improved master theorem for divide-and-conquer recurrences. In: Degano, P., Gorrieri, R., Marchetti-Spaccamela, A. (eds) Automata, Languages and Programming. ICALP 1997. Lecture Notes in Computer Science, vol 1256. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63165-8_201

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  • DOI: https://doi.org/10.1007/3-540-63165-8_201

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63165-1

  • Online ISBN: 978-3-540-69194-5

  • eBook Packages: Springer Book Archive

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