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How to aggregate Top-lists: Score based approximation schemes

by   Claire Mathieu, et al.

We study the aggregation of partial rankings and give a PTAS for TOP-AGG, the problem of aggregating a collection of top-lists into a single full-ranking. When the input top-lists all have length less than some fixed constant, we provide an EPTAS. In terms of technical contributions, an important notion is the score of a candidate, namely, the number of times it has been selected by voters: low-score candidates can be sorted by score at the end of the output without deteriorating its quality by much. Another important observation is that an optimal output never differs too much from the sorted order, in the sense that in any optimal ranking, a candidate with score smaller than one fourth of the score of another candidate is ranked after that latter candidate.


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