Oblivious and Adaptive Strategies for the Majority and Plurality Problems

摘要

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.