Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 pi and a specific ight wi,  would like to divide the elements into m mutually exclusive groups such that the sum over all the groups of the average group ight is maximal.  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 minwi < α < β â¤ maxwi, such that all the elements with ight wi satisfying α â¤ wi â¤ 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.
['Shmuel Gal', 'Boris Klots']
I am writing a research paper on a idea Optimal Partitioning Which Maximizes the Sum of the Weighted Averages
[{"from": "human", "value": "I am writing a research paper on a idea Optimal Partitioning Which Maximizes the Sum of the Weighted Averages"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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 pi and a specific ight wi,  would like to divide the elements into m mutually exclusive groups such that the sum over all the groups of the average group ight is maximal.  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 \u03b1 and \u03b2, with minwi < \u03b1 < \u03b2 \u00e2\u0089\u00a4 maxwi, such that all the elements with ight wi satisfying \u03b1 \u00e2\u0089\u00a4 wi \u00e2\u0089\u00a4 \u03b2 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."}]