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Choosing Subsets with Maximum Weighted Average (1997) [2 citations — 1 self]

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@TECHREPORT{Eppstein97choosingsubsets,
    author = {David Eppstein and Daniel S. Hirschberg},
    title = {Choosing Subsets with Maximum Weighted Average},
    institution = {Journal of Algorithms},
    year = {1997}
}

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Abstract:

Given a set of n real values, each with a positive weight, we wish to find the subset of n - k values having maximum weighted average. This is equivalent to the following form of parametric selection: given n objects with values decreasing linearly with time, find the time at which the n - k maximum values add to zero. We show that these problems can be solved in time O(n) (independent of k). A generalization in which weights are allowed to be negative is NP-complete. 1 Introduction A common policy in grading coursework allows students to drop a single homework score. The remaining scores are then combined in some kind of weighted average to determine the student's grade. The problem of performing such calculations automatically has an easy linear time solution: simply try each set of n - 1 scores. The average for each set can be computed in constant time from the sums of all scores and of all weights. Consider the generalization of this problem in which not one but two s...

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