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- W4313443311 abstract "We present an almost optimal algorithm for the classic Chamberlin-Courant multiwinner voting rule (CC) on single-peaked preference profiles. Given $n$ voters and $m$ candidates, it runs in almost linear time in the input size, improving the previous best $O(nm^2)$ time algorithm of Betzler et al. (2013). We also study multiwinner voting rules on nearly single-peaked preference profiles in terms of the candidate-deletion operation. We show a polynomial-time algorithm for CC where a given candidate-deletion set $D$ has logarithmic size. Actually, our algorithm runs in $2^{|D|} cdot poly(n,m)$ time and the base of the power cannot be improved under the Strong Exponential Time Hypothesis. We also adapt these results to all non-constant Thiele rules which generalize CC with approval ballots." @default.
- W4313443311 created "2023-01-06" @default.
- W4313443311 creator A5005932872 @default.
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- W4313443311 date "2022-12-28" @default.
- W4313443311 modified "2023-10-18" @default.
- W4313443311 title "Near-Tight Algorithms for the Chamberlin-Courant and Thiele Voting Rules" @default.
- W4313443311 doi "https://doi.org/10.48550/arxiv.2212.14173" @default.
- W4313443311 hasPublicationYear "2022" @default.
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