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Periodica Mathematica Hungarica

, Volume 64, Issue 1, pp 101–117 | Cite as

Number of survivors in the presence of a demon

  • Guy Louchard
  • Helmut Prodinger
  • Mark Daniel Ward
Article

Abstract

This paper complements the analysis of Louchard and Prodinger [LP08] on the number of rounds in a coin-flipping selection algorithm that occurs in the presence of a demon. We precisely analyze a very different aspect of the selection algorithm, using different methods of analysis. Specifically, we obtain precise descriptions of the distribution and all moments of the number of participants ultimately selected during the execution of the algorithm. The selection algorithm is robust in at least two significant ways. The presence of a demon allows for the precise analysis even when errors may occur between the rounds of the selection process. (The analysis also handles the more traditional case, in which no demon is involved.) The selection algorithm can also use either biased or unbiased coins.

Key words and phrases

analysis of algorithms leader election coin flip survivor demon asymptotic approximation trie q-Pochhammer symbol factorial moment distribution generating function recurrence poissonization 

Mathematics subject classification numbers

05A16 05A30 60C05 68W20 68W40 

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References

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    P. Flajolet and R. Sedgewick, Mellin transforms and asymptotics: Finite differences and Rice’s integrals, Theoret. Comput. Sci., 144 (1995), 101–124.MathSciNetMATHCrossRefGoogle Scholar
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    P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge, 2009.Google Scholar
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    M. Loève, Probability Theory (2 volumes), 4th edition, Springer, New York, 1977, 1978.MATHGoogle Scholar
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    G. Louchard and H. Prodinger, Advancing in the presence of a demon, Math. Slovaca, 58 (2008), 263–276.MathSciNetMATHCrossRefGoogle Scholar
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    W. Szpankowski, Average Case Analysis of Algorithms on Sequences, Wiley, New York, 2001.MATHCrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2012

Authors and Affiliations

  • Guy Louchard
    • 1
  • Helmut Prodinger
    • 2
  • Mark Daniel Ward
    • 3
  1. 1.Département d’InformatiqueUniversité Libre de BruxellesBruxellesBelgium
  2. 2.Department of MathematicsUniversity of StellenboschStellenboschSouth Africa
  3. 3.Department of StatisticsPurdue UniversityWest LafayetteUSA

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