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Irrelevant matches in round-robin tournaments
Autonomous Agents and Multi-Agent Systems ( IF 2.0 ) Pub Date : 2020-11-13 , DOI: 10.1007/s10458-020-09483-6
Marco Faella , Luigi Sauro

We consider tournaments played by a set of players in order to establish a ranking among them. We introduce the notion of irrelevant match, as a match that does not influence the ultimate ranking of the involved parties. After discussing the basic properties of this notion, we seek out tournaments that have no irrelevant matches, focusing on the class of tournaments where each player challenges each other exactly once. We prove that tournaments with a static schedule and at least five players always include irrelevant matches. Conversely, dynamic schedules for an arbitrary number of players can be devised that avoid irrelevant matches, at least for one of the players involved in each match. Finally, we prove by computational means that there exist tournaments where all matches are relevant to both players, at least up to eight players.



中文翻译:

循环锦标赛中不相关的比赛

我们考虑由一组玩家参加的锦标赛,以便在其中排名。我们引入不相关匹配的概念,因为这种匹配不会影响相关方的最终排名。在讨论了此概念的基本属性之后,我们将找出没有无关紧要的比赛,重点是每个球员相互挑战一次的比赛类别。我们证明了时间表固定且至少有五名球员的比赛总是包括无关紧要的比赛。相反地​​,可以设计用于任意数量的球员的动态时间表,以避免至少在每次比赛中所涉及的一位球员不相关的比赛。最后,我们通过计算方式证明存在一些比赛,所有比赛都与这两名球员相关,至少有八名球员。

更新日期:2020-11-15
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