{"type":"ScholarlyArticle","title":"When Rigging a Tournament, Let Greediness Blind You","authors":[{"name":"Sushmita Gupta","slug":"sushmita-gupta","given":"Sushmita","family":"Gupta","affiliation":"University of Bergen , Bergen , Norway"},{"name":"Sanjukta Roy","slug":"sanjukta-roy","given":"Sanjukta","family":"Roy","affiliation":"The Institute of Mathematical Sciences , HBNI , Chennai , India"},{"name":"Saket Saurabh","slug":"saket-saurabh","given":"Saket","family":"Saurabh","affiliation":"University of Bergen , Bergen , Norway"},{"name":"Meirav Zehavi","slug":"meirav-zehavi","given":"Meirav","family":"Zehavi","affiliation":"The Institute of Mathematical Sciences , HBNI , Chennai , India; Ben-Gurion University , Beersheba , Israel"}],"abstract":"A knockout tournament is a standard format of competition, ubiquitous in sports, elections and decision making. Such a competition consists of several rounds. In each round, all players that have not yet been eliminated are paired up into matches. Losers are eliminated, and winners are raised to the next round, until only one winner exists. Given that we can correctly predict the outcome of each potential match (modelled by a tournament D), a seeding of the tournament deterministically determines its winner. Having a favorite player v in mind, the Tournament Fixing Problem (TFP) asks whether there exists a seeding that makes v the winner. Aziz et al. [AAAI’14] showed that TFP is NP-hard. They initiated the study of the parameterized complexity of TFP with respect to the feedback arc set number k of D, and gave an XP-algorithm (which is highly inefficient). Recently, Ramanujan and Szeider [AAAI’17] showed that TFP admits an FPT algorithm, running in time 2^{ O(k^2 log k)} n ^{O(1)}. At the heart of this algorithm is a translation of TFP into an algebraic system of equations, solved in a black box fashion (by an ILP solver). We present a fresh, purely combinatorial greedy solution. We rely on new insights into TFP itself, which also results in the better running time bound of 2^{ O(k log k)} n^{ O(1)} . While our analysis is intricate, the algorithm itself is surprisingly simple.","doi":"10.24963/ijcai.2018/38","url":"https://ijcai.org/proceedings/2018/38","pdf":"https://ijcai.org/proceedings/2018/0038.pdf","markdown":"https://ijcai.org/proceedings/2018/38.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/38","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":38,"pages":{"first":275,"last":281},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Voting"],"videos":[],"references":[{"position":1,"raw":"[Aziz et al., 2014] Aziz, Gaspers, Mackenzie, Mattei, Sturs- berg, and Walsh. 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