Majority and plurality problems

Authors:
DáNiel Gerbner;Gyula O. H. Katona;DöMöTöR PáLvöLgyi;BaláZs PatkóS
Affiliations:
Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15 Budapest, 1053, Hungary;Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15 Budapest, 1053, Hungary;Eötvös Loránd University, Department of Computer Science, Pázmány Péter sétány 1/D Budapest, 1117, Hungary;Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15 Budapest, 1053, Hungary
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 3
Cited 0

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Abstract

Given a set of n balls each colored with a color, a ball is said to be a majority, k-majority, or plurality ball if its color class has size larger than half of the number of balls, has size at least k, or has size larger than any other color class, respectively. We address the problem of finding the minimum number of queries (comparisons of a pair of balls as regards whether they have the same color or not) needed to decide whether a majority, k-majority or plurality ball exists and, if it does, then to show one such ball. We consider both adaptive and non-adaptive strategies and, for certain cases, we also address weighted versions of the problems.