Single-elimination (SE) tournaments are a popular format used in competitive environments and decision making. Algorithms for SE tournament manipulation have been an active topic of research in recent years. In this paper, we initiate the algorithmic study of a novel variant of SE tournament manipulation that aims to model the fact that certain matchups are highly desired in a sporting context, incentivizing an organizer to manipulate the bracket to make such matchups take place. We obtain both hardness and tractability results. We show that while the problem of computing a bracket enforcing a given set of matches in an SE tournament is NP-hard, there are natural restrictions that lead to polynomial-time solvability. In particular, we show polynomial-time solvability if there is a linear ordering on the ability of players with only a constant number of exceptions where a player with lower ability beats a player with higher ability.

翻译：单败淘汰（SE）锦标赛是竞技环境和决策制定中广泛采用的一种形式。近年来，针对SE锦标赛操控的算法研究已成为一个活跃的研究课题。本文首次从算法角度研究了一种新的SE锦标赛操控变体，旨在模拟体育赛事中某些对阵极其理想的情况，从而激励组织者通过操纵赛程来促成这些对阵。我们获得了难度性与可解性两方面的结论。研究表明，尽管在SE锦标赛中计算一个能强制实现给定对阵集合的赛程属于NP难题，但某些自然限制条件能够实现多项式时间可解性。特别地，当选手能力存在线性排序且仅有常数次例外（即低能力选手击败高能力选手的情况）时，我们证明了该问题的多项式时间可解性。