Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding a non-minority ball with majority answers   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.

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The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
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The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom