Periodica Mathematica Hungarica
Volume/Issue:
Volume 64: Issue 1
Number of survivors in the presence of a demon
Authors:
Guy Louchard Département d’Informatique, Université Libre de Bruxelles, CP 212, Boulevard du Triomphe, B-1050 Bruxelles, Belgium

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Helmut Prodinger Department of Mathematics, University of Stellenbosch, 7602 Stellenbosch, South Africa

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Mark Ward Department of Statistics, Purdue University, 150 North University St., West Lafayette, IN 47907-2067, USA

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Pages:
101–117
Online Publication Date:
30 Jan 2012
Publication Date:
01 Mar 2012
Article Category:
Research Article
DOI:
https://doi.org/10.1007/s10998-012-9101-9
Keywords:
05A16; 05A30; 60C05; 68W20; 68W40; analysis of algorithms; leader election; coin flip; survivor; demon; asymptotic; approximation; trie; q-Pochhammer symbol; factorial moment; distribution; generating function; recurrence; poissonization
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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.

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Cover Periodica Mathematica Hungarica
Periodica Mathematica Hungarica
Print ISSN:
0031-5303
Online ISSN:
1588-2829

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation		 1971
Volumes
per Year		 2
Issues
per Year		 4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address		 H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address		 H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher		 Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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