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May 1997 Determining the majority: the biased case
Philippe Chassaing
Ann. Appl. Probab. 7(2): 523-544 (May 1997). DOI: 10.1214/aoap/1034625343

Abstract

We are given a set of n elements, some of them red, the others blue, but their colors are hidden. We are to determine the composition of this set, or to determine an element of the majority color, by making pairwise comparisons of elements from which we obtain the information "the colors of these two elements are the same," or "they are different." Let $\tau_n$, respectively, $\mu_n$, be the optimal average number of comparisons needed to solve these two problems. We give an explicit expression of the limit of $\tau_n /n$, respectively, of $\mu_n /n$, in terms of the probabilities of being red or blue. We also discuss quasi-optimal algorithms in both cases: when these probabilities are known and when they are unknown.

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Philippe Chassaing. "Determining the majority: the biased case." Ann. Appl. Probab. 7 (2) 523 - 544, May 1997. https://doi.org/10.1214/aoap/1034625343

Information

Published: May 1997
First available in Project Euclid: 14 October 2002

zbMATH: 0876.68057
MathSciNet: MR1442325
Digital Object Identifier: 10.1214/aoap/1034625343

Subjects:
Primary: 68Q25 , 90C15
Secondary: 90C40 , 93E20

Keywords: Bellman principle , connected component , graph , martingale , quasi-optimal algorithm

Rights: Copyright © 1997 Institute of Mathematical Statistics

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Vol.7 • No. 2 • May 1997
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