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The new FIFA rules are hard: complexity aspects of sports competitions

Kern, W.; Paulusma, D.

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Authors

W. Kern



Abstract

Consider a soccer 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 complexity of this question depends on the way scores are allocated according to the outcome of a match. For example, the problem is polynomially solvable for the ancient FIFA rules ( resp. ) but becomes NP-hard if the new rules ( resp. ) are applied. We determine the complexity of the above problem for all possible score allocation rules.

Citation

Kern, W., & Paulusma, D. (2001). The new FIFA rules are hard: complexity aspects of sports competitions. Discrete Applied Mathematics, 108(3), 317-323. https://doi.org/10.1016/s0166-218x%2800%2900241-9

Journal Article Type Article
Publication Date Mar 1, 2001
Deposit Date Dec 20, 2014
Publicly Available Date Mar 29, 2024
Journal Discrete Applied Mathematics
Print ISSN 0166-218X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 108
Issue 3
Pages 317-323
DOI https://doi.org/10.1016/s0166-218x%2800%2900241-9
Keywords NP-complete; Network flow.
Public URL https://durham-repository.worktribe.com/output/1414988

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Discrete applied mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete applied mathematics, 108/3, 2001, 10.1016/S0166-218X(00)00241-9





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