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

Walter Kern, Daniël Paulusma

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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.
Original languageUndefined
Place of PublicationEnschede
PublisherUniversiteit Twente
Number of pages9
ISBN (Print)0169-2690
Publication statusPublished - 1999

Publication series

NameMemorandum / Faculty of Mathematical Sciences
PublisherDepartment of Applied Mathematics, University of Twente
No.1505
ISSN (Print)0169-2690

Keywords

  • MSC-03D15
  • EWI-3325
  • IR-65693
  • METIS-141287
  • MSC-90C27

Cite this

Kern, W., & Paulusma, D. (1999). The new FIFA rules are hard: Complexity aspects of sports competitions. (Memorandum / Faculty of Mathematical Sciences; No. 1505). Enschede: Universiteit Twente.
Kern, Walter ; Paulusma, Daniël. / The new FIFA rules are hard: Complexity aspects of sports competitions. Enschede : Universiteit Twente, 1999. 9 p. (Memorandum / Faculty of Mathematical Sciences; 1505).
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Kern, W & Paulusma, D 1999, The new FIFA rules are hard: Complexity aspects of sports competitions. Memorandum / Faculty of Mathematical Sciences, no. 1505, Universiteit Twente, Enschede.

The new FIFA rules are hard: Complexity aspects of sports competitions. / Kern, Walter; Paulusma, Daniël.

Enschede : Universiteit Twente, 1999. 9 p. (Memorandum / Faculty of Mathematical Sciences; No. 1505).

Research output: Book/ReportReportProfessional

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N2 - 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.

AB - 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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KW - IR-65693

KW - METIS-141287

KW - MSC-90C27

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Kern W, Paulusma D. The new FIFA rules are hard: Complexity aspects of sports competitions. Enschede: Universiteit Twente, 1999. 9 p. (Memorandum / Faculty of Mathematical Sciences; 1505).