{"type":"ScholarlyArticle","title":"Near-Tight Algorithms for the Chamberlin-Courant and Thiele Voting Rules","authors":[{"name":"Krzysztof Sornat","slug":"krzysztof-sornat","given":"Krzysztof","family":"Sornat","affiliation":"AGH University , Poland"},{"name":"Virginia Vassilevska Williams","slug":"virginia-vassilevska-williams","given":"Virginia Vassilevska","family":"Williams","affiliation":"postdoc at MIT CSAIL , USA."},{"name":"Yinzhan Xu","slug":"yinzhan-xu","given":"Yinzhan","family":"Xu","affiliation":"MIT CSAIL , USA"}],"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. 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| * 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.","doi":"10.24963/ijcai.2022/69","url":"https://ijcai.org/proceedings/2022/69","pdf":"https://ijcai.org/proceedings/2022/0069.pdf","markdown":"https://ijcai.org/proceedings/2022/69.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/69","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":69,"pages":{"first":482,"last":488},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986935","length_sec":82,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985078","length_sec":346,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Aggarwal and Park, 1988] A. 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