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## The Structure and Complexity of Sports Elimination Numbers (1999)

Venue: | Algorithmica |

Citations: | 10 - 0 self |

### Citations

2792 | Computational complexity
- Papadimitriou
- 1994
(Show Context)
Citation Context ...from the playoffs is NP-complete in the classic setting. Proof. The reduction is from the version of 3-SAT where each clause has two or three variables and each literal appears in at most two clauses =-=[Pap94]-=-. Given a formula F with k distinct variables (where each variable is assumed to appear both negated and unnegated in F ) and c clauses, we create an instance of a k + 1-division baseball problem. It ... |

17 | Fast algorithms for parametric scheduling come from extensions to parametric maximum flow
- McCormick
(Show Context)
Citation Context ...oes i? Question Q1 was shown in [GM92] to be solvable in time proportional to a single network flow, provided the number of remaining games is O(2 n 2 ). McCormick eliminated the later requirement in =-=[McC96]-=-. However, the constructive method in [Way] implies that the answer to question Q1 is W for every team i where W (i)sW . Hence no additional computation is needed for Q1, once the classic elimination ... |

14 |
A fast algorithm for the generalized parametric minimum cut problem and applications
- Gusfield, Martel
- 1992
(Show Context)
Citation Context ...east one scenario? 3. Q3 For team i, is there a scenario where i can at least tie for k'th position, i.e., where at most k \Gamma 1 teams win strictly more games than does i? Question Q1 was shown in =-=[GM92]-=- to be solvable in time proportional to a single network flow, provided the number of remaining games is O(2 n 2 ). McCormick eliminated the later requirement in [McC96]. However, the constructive met... |

13 |
Possible winners in partially completed tournaments
- Schwartz
- 1990
(Show Context)
Citation Context ...or the remaining games, which teams will necessarily win fewer total games than some other team. This problem goes back more than thirty years to Alan Hoffman and T. Rivlin [HR70], and to B. Schwartz =-=[Sch66]-=-; it is widely used to illustrate linear programming and network flow 1 . For team i, w(i) denotes the number of games already won, and g(i) is the number of remaining games to be played. In the class... |

7 | A new property and a faster algorithm for baseball elimination
- Wayne
(Show Context)
Citation Context ...pplication 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 ... |

4 |
A fast parametric network flow algorithm and applications
- Gallo, Grigoriadis, et al.
- 1989
(Show Context)
Citation Context ...ity Each network WILD (for a combination of division winners) is a linear monotone parametric flow network, so we can find the minimum value of W saturating all arcs out of s in the time for one flow =-=[GGT89]-=-. In the worst case there could be (n=k) k combinations, but by first computing possible division winners within each division (at a cost of the time for one flow/division), we will usually be able to... |

2 |
When is a team "mathematically" eliminated
- Hoffman, Rivlin
- 1970
(Show Context)
Citation Context ...r every win/loss scenario for the remaining games, which teams will necessarily win fewer total games than some other team. This problem goes back more than thirty years to Alan Hoffman and T. Rivlin =-=[HR70]-=-, and to B. Schwartz [Sch66]; it is widely used to illustrate linear programming and network flow 1 . For team i, w(i) denotes the number of games already won, and g(i) is the number of remaining game... |

1 |
optimization and the world wide web. unpublished manuscript
- Baseball
- 1998
(Show Context)
Citation Context ... 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... |

1 |
Football elimination is hard to decide under the 3-point rule. unpublished manuscript
- Burnholt, Gullich, et al.
- 1999
(Show Context)
Citation Context ...ity p i;j that team i will win the game, and 5 We recently learned that the elimination problem for the European football scoring scheme, mentioned in Section 2, has also been shown to be NP-complete =-=[BGHS]-=-, even though (as shown in Section 2) there is a single elimination threshold for that scoring scheme. probability p j;i = 1 \Gamma p i;j that team j will win the game 6 . We first show that the probl... |