Balanced Partition of a Graph for Football Team Realignment in Ecuador
In the second category of the Ecuadorian football league, a set of football teams must be grouped into \(k\) geographical zones according to some regulations, where the total distance of the road trips that all teams must travel to play a Double Round Robin Tournament in each zone is minimized. This problem can be modeled as a \(k\)-clique partitioning problem with constraints on the sizes and weights of the cliques. An integer programming formulation and a heuristic approach were developed to provide a solution to the problem which has been implemented in the 2015 edition of the aforementioned football championship.
KeywordsInteger programming models Graph partitioning Heuristics Football
We thank Patricio Torres, authority of the team Liga Deportiva Universitaria, and Galo Barreto, former manager of AFNA, for their support to this project. This research was partially supported by the PACK-COVER MATH-AmSud cooperation project.
- 4.Furmanczyk, H., Kubale, M.: Equitable coloring of graphs. In: Graph Colorings, Providence, Rhode Island, pp. 35–53. American Mathematical Society (2004)Google Scholar
- 6.McDonald, B., Pulleyblank, W.: Realignment in the NHL, MLB, NFL, and NBA. J. Quant. Anal. Sports 10, 225–240 (2014)Google Scholar
- 7.Mitchell, J.: Branch-and-cut for the k-way equipartition problem. Technical report, Department of Mathematical Sciences, Rensselaer Polytechnic Institute (2001)Google Scholar
- 12.Test instances for the football team realignment in Ecuador. http://www.math.epn.edu.ec/~recalde/#TestInstances/