We use cookies to ensure that we give you the best experience on our website. By continuing to browse this repository, you give consent for essential cookies to be used. You can read more about our Privacy and Cookie Policy.

Durham Research Online
You are in:

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

Kern, W. and Paulusma, D. (2001) 'The new FIFA rules are hard : complexity aspects of sports competitions.', Discrete applied mathematics., 108 (3). pp. 317-323.


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.

Item Type:Article
Keywords:NP-complete; Network flow.
Full text:(AM) Accepted Manuscript
Download PDF
Publisher Web site:
Publisher 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
Date accepted:No date available
Date deposited:08 January 2015
Date of first online publication:March 2001
Date first made open access:No date available

Save or Share this output

Look up in GoogleScholar