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

Walter Kern, Daniël Paulusma

Research output: Contribution to journalArticleAcademicpeer-review

19 Citations (Scopus)
56 Downloads (Pure)


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 languageEnglish
Pages (from-to)317-323
Number of pages7
JournalDiscrete applied mathematics
Issue number3
Publication statusPublished - 2001


  • Network Flow
  • NP-complete


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