Determining plurality

Alonso, Laurent; Reingold, Edward M.

doi:10.1145/1367064.1367066

Cited by 8 publications

(5 citation statements)

References 16 publications

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“…The mode algorithms mentioned above can verify the uniqueness of the mode without any asymptotic increase in time. Numerous results established bounds on the number of comparisons required for computing a majority, α-majority, mode, or plurality (e.g., [1,2,11,21]).…”

Section: Related Workmentioning

confidence: 99%

Range Majority in Constant Time and Linear Space

Durocher

Munro

et al. 2011

Automata, Languages and Programming

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Given an array A of size n, we consider the problem of answering range majority queries: given a query range [i..j] where 1 ≤ i ≤ j ≤ n, return the majority element of the subarray A[i..j] if it exists. We describe a linear space data structure that answers range majority queries in constant time. We further generalize this problem by defining range α-majority queries: given a query range [i..j], return all the elements in the subarray A[i..j] with frequency greater than α(j − i + 1). We prove an upper bound on the number of α-majorities that can exist in a subarray, assuming that query ranges are restricted to be larger than a given threshold. Using this upper bound, we generalize our range majority data structure to answer range α-majority queries in O( 1 α ) time using O(n lg( 1 α + 1)) space, for any fixed α ∈ (0, 1). This result is interesting since other similar range query problems based on frequency have nearly logarithmic lower bounds on query time when restricted to linear space.

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Section: Related Workmentioning

confidence: 99%

Range Majority in Constant Time and Linear Space

Durocher

Munro

et al. 2011

Automata, Languages and Programming

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“…We also remark that without such an assumption, a quadratic lower bound can be proven to be very close to the worst-case n 2 upper bound using similar arguments as in the proof of Theorem 2 in Section 3. 4 In fact, this quadratic lower bound can also be extended to the general case where the goal is to identify a ball whose color has appeared more than t ≥ n/2 times. PROOF.…”

Section: Oblivious Strategy For the Majority Problemmentioning

confidence: 99%

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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“…Since then many research was carried out about the Plurality problem, see e.g. [2,3,4,5,7,10,11,16]. In [7] it is written, that "[The Plurality problem] seems to be a more difficult variant".…”

Section: Introductionmentioning

confidence: 99%

A plurality problem with three colors and query size three

Gerbner¹,

Dániel²,

Vizer³

2017

Preprint

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The Plurality problem -introduced by Aigner [1] -has many variants. In this article we deal with the following version: suppose we are given n balls, each of them colored by one of three colors. A plurality ball is one such that its color class is strictly larger than any other color class. Questioner wants to find a plurality ball as soon as possible or state there is no, by asking triplets (or k-sets, in general), while Adversary partition the triplets into color classes as

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Determining plurality

Cited by 8 publications

References 16 publications

Range Majority in Constant Time and Linear Space

Range Majority in Constant Time and Linear Space

Oblivious and Adaptive Strategies for the Majority and Plurality Problems

A plurality problem with three colors and query size three

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