Discrete Mathematics
An algorithm to generate tournament score sequences
Mathematical and Computer Modelling: An International Journal
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In this paper, we deal with the issue of determining the scores of all matches involved in a football tournament. The final table of the tournament, which shows the standings of the teams, is taken as the initial data of the problem. This is a different kind of combinatorial problems which require the construction of valid initial states according to some given final state. We use a rules-based method to solve the problem, analyzing the search space and introducing the notion of black&white graphs. The table data is firstly used to compute possible results of all played matches. Based on the results as well as the total number of scored and conceded goals, possible scores of the matches are then computed. The solution strategy is experimented on several final tables from previous World Cup tournaments. Other experiments are conducted for various team standings, measuring the time required to process some specific data of up to 10 teams.