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


Kern, Walter and Paulusma, Daniël (2001) The new FIFA rules are hard: complexity aspects of sports competitions. Discrete Applied Mathematics, 108 (3). pp. 317-323. ISSN 0166-218X

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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 (2 : 0 resp. 1 : 1) but becomes NP-hard if the new rules (3 : 0 resp. 1 : 1) are applied. We determine the complexity of the above problem for all possible score allocation rules.
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Copyright:© 2001 Elsevier
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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