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On more variants of the Majority Problem

Abstract : The variant of the Majority problem we are considering is the following. A colorblind player is given a set of colored balls. He knows that each ball is colored either red or green, and that there are less green than red balls, but he cannot distinguish the two colors. For any two balls he can ask whether they are colored the same. His goal is to determine the color of each of the balls, asking as few questions as possible. In the case where there are at most (respectively exactly ) green balls, the minimum number of questions that guarantees the determination of the colors is denoted by (respectively ). We extend results of Aigner on exact values of , and we provide upper bounds for , and even exact values for the first two values of p. Our results lead to several new questions.
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Submitted on : Monday, October 25, 2021 - 3:04:41 PM
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Myriam Preissmann, Paul-Elliot Angles d'Auriac, Francis Maisonneuve, Vivien Maisonneuve, Emmanuel Preissmann. On more variants of the Majority Problem. Discrete Applied Mathematics, Elsevier, 2019, 265, pp.1-12. ⟨10.1016/j.dam.2019.03.030⟩. ⟨hal-02148478⟩



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