An Exercise in Tournament Design: When Some Matches Must Be Scheduled
CoRR(2024)
摘要
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.
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