The William Lowell Putnam mathematical competition: problems and solutions: 1965-1984
The William Lowell Putnam mathematical competition: problems and solutions: 1965-1984
Information Processing Letters
The Average-Case Complexity of Determining the Majority
SIAM Journal on Computing
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The plurality problem with three colors and more
Theoretical Computer Science
Information Processing Letters
Probabilistic strategies for the partition and plurality problems
Random Structures & Algorithms - Proceedings from the 12th International Conference “Random Structures and Algorithms”, August1-5, 2005, Poznan, Poland
ACM Transactions on Algorithms (TALG)
Average-case lower bounds for the plurality problem
ACM Transactions on Algorithms (TALG)
Randomized strategies for the plurality problem
Discrete Applied Mathematics
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Given a set of n elements, each of which is colored one of c colors, we must determine an element of the plurality (most frequently occurring) color by pairwise equal/unequal color comparisons of elements. We focus on the expected number of color comparisons when the cn colorings are equally probable. We analyze an obvious algorithm, showing that its expected performance is c2 + c − 2/2c n − O(c2), with variance Θ(c2n). We present and analyze an algorithm for the case c = 3 colors whose average complexity on the 3n equally probable inputs is 7083/5425n + O(&sqrt;n) = 1.3056…n + O(&sqrt; n), substantially better than the expected complexity 5/3n + O(1) = 1.6666…n + O(1) of the obvious algorithm. We describe a similar algorithm for c =4 colors whose average complexity on the 4n equally probable inputs is 761311/402850n + O(log n) = 1.8898…n + O(log n), substantially better than the expected complexity 9/4n + O(1) = 2.25n + O(1) of the obvious algorithm.