Combinatorial optimization
The new FIFA rules are hard: complexity aspects of sports competitions
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A New Property and a Faster Algorithm for Baseball Elimination
SIAM Journal on Discrete Mathematics
Football Elimination Is Hard to Decide Under the 3-Point-Rule
MFCS '99 Proceedings of the 24th International Symposium on Mathematical Foundations of Computer Science
Manipulating Tournaments in Cup and Round Robin Competitions
ADT '09 Proceedings of the 1st International Conference on Algorithmic Decision Theory
Mathematically clinching a playoff spot in the NHL and the effect of scoring systems
Canadian AI'08 Proceedings of the Canadian Society for computational studies of intelligence, 21st conference on Advances in artificial intelligence
Possible and necessary winners of partial tournaments
Proceedings of the 11th International Conference on Autonomous Agents and Multiagent Systems - Volume 2
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Consider a sports competition among various teams playing against each other in pairs (matches) according to a previously determined schedule. At some stage of the competition one may ask whether a particular team still has a (theoretical) chance to win the competition. The computational complexity of this question depends on the way scores are allocated according to the outcome of a match. For competitions with at most 3 different outcomes of a match the complexity is already known. In practice there are many competitions in which more than 3 outcomes are possible. We determine the complexity of the above problem for competitions with an arbitrary number of different outcomes. Our model also includes competitions that are asymmetric in the sense that away playing teams possibly receive other scores than home playing teams.