Computing Majority with Triple Queries

TL;DR

This paper studies the problem of determining the majority color among n balls using only triple queries, providing algorithms and tight bounds for the minimum number of queries needed in different models.

Contribution

It introduces algorithms and tight bounds for the minimum number of triple queries required to find the majority color in two different computational models.

Findings

Algorithms for minimum 3-queries to find majority

Tight bounds established for query complexity

Results depend on the query response model

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.