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The Structure and Complexity of Sports Elimination Numbers (1999)
| Venue: | Algorithmica |
| Citations: | 10 - 0 self |
BibTeX
@ARTICLE{Gusfield99thestructure,
author = {Dan Gusfield and Dan Gusfield and Chip Martel and Chip Martel},
title = {The Structure and Complexity of Sports Elimination Numbers},
journal = {Algorithmica},
year = {1999},
volume = {32},
pages = {2002}
}
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Abstract
Identifying the teams that are already eliminated from contention for first place of a sports league, is a classic problem that has been widely used to illustrate the application of linear programming and network flow. In the classic setting each game is played between two teams and the first place goes to the team with the greatest total wins. 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 (has no chance to win or tie for first place) if and only if it cannot win W or more games. They used this threshold to speed up the identification of eliminated teams. In both papers, the proofs of the existence the threshold are tied to the computational methods used to find it. In this paper we show that thresholds exist for a wide range of elimination problems (greatly generalizing the classical setting), via a simpler proof not connected to any partic...
