Choosing Subsets with Maximum Weighted Average

Given a set ofnreal values, each with a positive weight, we wish to find the subset ofn?kvalues having maximum weighted average. This is equivalent to the following form of parametric selection: givennobjects with values decreasing linearly with time, find the time at which then?kmaximum values add to zero. We show that these problems can be solved in timeO(n) (independent ofk). A generalization in which weights are allowed to be negative is NP-complete.

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