Abstract
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. 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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References
Aigner, M.: Variants of the Majority Problem. Applied Discrete Mathematics 137, 3–25 (2004)
Aigner, M., De Marco, G., Montangero, M.: The Plurality Problem with Three Colors. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 513–521. Springer, Heidelberg (2004)
Aigner, M., De Marco, G., Montangero, M.: The Plurality Problem with Three Colors and More. Theoretical Computer Science (2005) (to appear)
Alon, N.: Eigenvalues and Expanders. Combinatorica 6, 86–96 (1986)
Alonso, L., Reingold, E., Schott, R.: Average-case Complexity of Determining the Majority. SIAM J. Computing 26, 1–14 (1997)
Blecher, P.M.: On a Logical Problem. Discrete Mathematics 43, 107–110 (1983)
Bollobás, B.: Random graphs, 2nd edn. Cambridge Studies in Advanced Mathematics, vol. 73. Cambridge University Press, Cambridge (2001)
Chung, F.R.K.: Spectral Graph Theory. CBMS Lecture Notes. AMS Publications, Providence (1997)
Chung, F.R.K., Graham, R.L., Mao, J., Yao, A.C.: Finding Favorites. In: Electronic Colloquium on Computational Complexity (ECCC), p–78 (2003)
Fischer, M.J., Salzberg, S.L.: Finding a Majority among n Votes. J. Algorithms 3, 375–379 (1982)
Knuth, D.E.: personal communication
Knuth, D.E.: The Art of Computer Programming, Volume 3. Sorting and Searching. Addison-Wesley Publishing Co., Reading (1973)
Lubotzky, A., Phillips, R., Sarnak, P.: Ramanujan Graphs. Combinatorica 8, 261–277 (1988)
Moore, J.: Proposed problem 81-5. J. Algorithms 2, 208–210 (1981)
Saks, M., Werman, M.: On Computing Majority by Comparisons. Combinatorica 11(4), 383–387 (1991)
Taylor, A., Zwicker, W.: personal communication
Wiener, G.: Search for a Majority Element. J. Statistical Planning and Inference 100, 313–318 (2002)
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Chung, F., Graham, R., Mao, J., Yao, A. (2005). Oblivious and Adaptive Strategies for the Majority and Plurality Problems. In: Wang, L. (eds) Computing and Combinatorics. COCOON 2005. Lecture Notes in Computer Science, vol 3595. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11533719_34
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DOI: https://doi.org/10.1007/11533719_34
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28061-3
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