作者
Martin Aigner, Gianluca De Marco, Manuela Montangero
发表日期
2005/6/9
期刊
Theoretical Computer Science
卷号
337
期号
1-3
页码范围
319-330
出版商
Elsevier
简介
The plurality problem is a game between two participants: Paul and Carole. We are given n balls, each of them is colored with one out of c colors. At any step of the game, Paul chooses two balls and asks whether they are of the same color, whereupon Carole answers yes or no. The game ends when Paul either produces a ball a of the plurality color (meaning that the number of balls colored like a exceeds those of the other colors), or when Paul states that there is no plurality. How many questions Lc(n) does Paul have to ask in the worst case? For c=2, the problem is equivalent to the well-known majority problem which has already been solved (Combinatorica 11 (1991) 383–387). In this paper we show that 3⌊n/2⌋-2⩽L3(n)⩽⌊5n/3⌋-2. Moreover, for any c⩽n, we show that surprisingly the naive algorithm for the plurality problem is asymptotically optimal.
引用总数
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学术搜索中的文章
M Aigner, G De Marco, M Montangero - Theoretical Computer Science, 2005