使用三重排序计算多数
Computing Majority with Triple Queries
摘要：
考虑一个包含用两种颜色着色的$n$球的箱子。在$k$查询中，$k$球由提问者选择，并且预言机的回复与该$k$元组中的球的颜色分布相关（取决于所考虑的计算模型）;然而，预言机从不揭示各个球的颜色。在一些查询之后，如果提问者可以输出多数颜色的球（如果它存在），则可以确定多数颜色，并且如果它不存在，则可以证明不存在多数。我们调查两种计算模型（取决于允许的回复类型）。我们给出的算法来计算的最小数量的3-查询，这是必要的，使提问者可以确定多数的颜色，并提供紧密和几乎紧密的上限和下限的查询需要在每种情况下的数量。
英文摘要：
Consider a bin containing $n$ balls colored with two colors. In a $k$-query, $k$ balls are selected by a questioner and the oracle's reply is related (depending on the computation model being considered) to the distribution of colors of the balls in this $k$-tuple; however, the oracle never reveals the colors of the individual balls. Following a number of queries the questioner is said to determine the majority color if it can output a ball of the majority color if it exists, and can prove that there is no majority if it does not exist. We investigate two computation models (depending on the type of replies being allowed). We give algorithms to compute the minimum number of 3-queries which are needed so that the questioner can determine the majority color and provide tight and almost tight upper and lower bounds on the number of queries needed in each case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
