Fixing Tournaments for Kings, Chokers, and More
نویسندگان
چکیده
We study the tournament fixing problem (TFP), which asks whether a tournament organizer can rig a single-elimination (SE) tournament such that their favorite player wins, simply by adjusting the initial seeding. Prior results give two perspectives of TFP: on the one hand, deciding whether an arbitrary player can win any SE tournament is known to be NP-complete; on the other hand, there are a number of known conditions, under which a player is guaranteed to win some SE tournament. We extend and connect both these lines of work. We show that for a number of structured variants of the problem, where our player is seemingly strong, deciding whether the player can win any tournament is still NP-complete. Dual to this hardness result, we characterize a new set of sufficient conditions for a player to win a tournament. Further, we give an improved exact algorithm for deciding whether a player can win a tournament.
منابع مشابه
On the 3-kings and 4-kings in multipartite tournaments
Koh and Tan gave a sufficient condition for a 3-partite tournament to have at least one 3-king in [K.M. Koh, B.P. Tan, Kings in multipartite tournaments, Discrete Math. 147 (1995) 171–183, Theorem 2]. In Theorem 1 of this paper, we extend this result to n-partite tournaments, where n 3. In [K.M. Koh, B.P. Tan, Number of 4-kings in bipartite tournaments with no 3-kings, Discrete Math. 154 (1996)...
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