The plurality problem with three colors and more

Aigner, Martin; Marco, Gianluca De; Montangero, Manuela

doi:10.1016/j.tcs.2004.12.035

Cited by 22 publications

(23 citation statements)

References 8 publications

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“…If Phase I ends in case (A), we use the induction hypothesis; in case (B), no more comparisons are needed because A i1 is a Plurality ball; in case (C), we need no more than r i more comparisons to identify A i1 or A i2 as a Plurality ball. In all cases, we can show (using the claim) with arguments similar to those in [2] that…”

Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 73%

“…Aigner et al [2] showed linear bounds for adaptive strategies for the Plurality problem with k = 3 colors. In this section we first note a linear upper bound for general k in this case, and then strengthen it using a generalized argument.…”

Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 99%

“…In [2] it was proved that P A 3 (n) ≤ 5 3 n − 2. We now give a generalized proof for all k ≥ 3 in this setting.…”

Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 99%

“…Detailed arguments are similar as in [2].) To prove the theorem, we use induction where the cases for n ≤ 3 are easy to verify.…”

Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 99%

“…One natural generalization is the so-called Plurality problem where the goal is to identify a ball of the dominant color (i.e., this color occurs more often than any other color). Linear upper and lower bounds were given for k = 3 colors for this variant in [2].…”

Section: Introductionmentioning

confidence: 99%

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Oblivious and Adaptive Strategies for the Majority and Plurality Problems

et al. 2007

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In the well-studied Majority problem, we are given a set of n balls colored with two or more colors, and the goal is to use the minimum number of color comparisons to find a ball of the majority color (i.e., a color that occurs for more than n/2 times). The Plurality problem has exactly the same setting while the goal is to find a ball of the dominant color (i.e., a color that occurs most often). Previous literature regarding this topic dealt mainly with adaptive strategies, whereas in this paper we focus more on the oblivious (i.e., non-adaptive) strategies. Given that our strategies are oblivious, we establish a linear upper bound for the Majority problem with arbitrarily many different colors assuming a majority label exists. We then show that the Plurality problem is significantly more difficult by establishing quadratic lower and upper bounds. In the end we also discuss some generalized upper bounds for adaptive strategies in the k-color Plurality problem.

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Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 73%

Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 99%

“…In [2] it was proved that P A 3 (n) ≤ 5 3 n − 2. We now give a generalized proof for all k ≥ 3 in this setting.…”

Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 99%

“…Detailed arguments are similar as in [2].) To prove the theorem, we use induction where the cases for n ≤ 3 are easy to verify.…”

Section: Adaptive Strategies For the Plurality Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Oblivious and Adaptive Strategies for the Majority and Plurality Problems

et al. 2007

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Probabilistic strategies for the partition and plurality problems

Dvořák¹,

Jelínek²,

Kráľ³

et al. 2006

Random Struct Algorithms

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ABSTRACT:We consider a game played by two players, Paul and Carol. Carol fixes a coloring of n balls with three colors. At each step, Paul chooses a pair of balls and asks Carol whether the balls have the same color. Carol truthfully answers yes or no. In the Plurality problem, Paul wants to find a ball with the most common color. In the Partition problem, Paul wants to partition the balls according to their colors. Paul's goal is to ask Carol the fewest number of questions to reach his goal. We find optimal probabilistic strategies for the Partition problem and the Plurality problem in the considered setting.

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