Optimal Partitioning Which Maximizes the Sum of the Weighted Averages
研究如何将一组带频率和权重的元素划分为多个互斥组，使得各组平均权重的总和最大，并给出多项式时间算法。
We consider an optimal partitioning problem that occurs in the assignment of computer jobs to a multiple cache and in other combinatorial optimization problems: For a given set of n elements, where each element i has a given frequency p i and a specific weight w i , we would like to divide the elements into m mutually exclusive groups such that the sum over all the groups of the average group weight is maximal. We characterize the optimal solution and present an algorithm which is polynomial in n for obtaining the optimal partitioning. Optimal partitioning policies for two groups has an especially simple characterization: There exist two numbers α and β, with minw i < α < β ≤ maxw i , such that all the elements with weight w i satisfying α ≤ w i ≤ β belong to one group and all other elements belong to the other group. A modification of this policy gives the optimal partitioning for an arbitrary number of groups.