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Mathematics > Combinatorics

arXiv:1509.08276 (math)
[Submitted on 28 Sep 2015 (v1), last revised 28 Sep 2016 (this version, v2)]

Title:Finding a non-minority ball with majority answers

Authors:Dániel Gerbner, Balázs Keszegh, Dömötör Pálvölgyi, Balázs Patkós, Máté Vizer, Gábor Wiener
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Abstract:Suppose we are given a set of $n$ balls $\{b_1,\ldots,b_n\}$ each colored either red or blue in some way unknown to us. To find out some information about the colors, we can query any triple of balls $\{b_{i_1},b_{i_2},b_{i_3}\}$. As an answer to such a query we obtain (the index of) a {\em majority ball}, that is, a ball whose color is the same as the color of another ball from the triple. Our goal is to find a {\em non-minority ball}, that is, a ball whose color occurs at least $\frac n2$ times among the $n$ balls. We show that the minimum number of queries needed to solve this problem is $\Theta(n)$ in the adaptive case and $\Theta(n^3)$ in the non-adaptive case. We also consider some related problems.
Subjects: Combinatorics (math.CO)
Cite as: arXiv:1509.08276 [math.CO]
  (or arXiv:1509.08276v2 [math.CO] for this version)
  https://doi.org/10.48550/arXiv.1509.08276

Submission history

From: Balázs Keszegh [view email]
[v1] Mon, 28 Sep 2015 11:22:54 UTC (28 KB)
[v2] Wed, 28 Sep 2016 13:09:34 UTC (29 KB)
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