Fast algorithms for parametric scheduling come from extensions to parametric maximum flow
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
A new property and a faster algorithm for baseball elimination
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
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Identifying teams eliminated from contention for first place of a sports league is a much studied problem. In the classic setting each game is played between two teams, and the team with the most wins finishes first. Recently, two papers [Way] and [AEHO] detailed a surprising structural fact in the classic setting: At any point in the season, there is a computable threshold W such that a team is eliminated (cannot win or tie for first place) if and only if it cannot win W or more games. Using this threshold speeds up the identification of eliminated teams. We show that thresholds exist for a wide range of elimination problems (greatly generalizing the classical setting), via a simpler and more direct proof. For the classic setting we determine which teams can be the strict winner of the most games; examine these issues for multi-division leagues with playoffs and wildcards; and establish that certain elimination questions are NP-hard.