Computing majority with triple queries

Authors:
Gianluca De Marco;Evangelos Kranakis;Gábor Wiener
Affiliations:
Dipartimento di Informatica e Applicazioni, Università di Salerno, Fisciano, Italy;School of Computer Science, Carleton University, Ottawa, ON, Canada;Department of Computer Science and Information Theory, Budapest University of Technology and Economics, Budapest, Hungary
Venue:
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
Year:
2011

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Abstract

Consider a bin containing n balls colored with two colors. In a k-query, k balls are selected by a questioner and the oracle's reply is related (depending on the computation model being considered) to the distribution of colors of the balls in this k-tuple; however, the oracle never reveals the colors of the individual balls. Following a number of queries the questioner is said to determine the majority color if it can output a ball of the majority color if it exists, and can prove that there is no majority if it does not exist. We investigate two computation models (depending on the type of replies being allowed). We give algorithms to compute the minimum number of 3-queries which are needed so that the questioner can determine the majority color and provide tight and almost tight upper and lower bounds on the number of queries needed in each case.