Combinatorial solutions to the Social Golfer Problem and Social Golfer Problem with Adjacent Group Sizes
arXiv:2507.23376
Abstract
Resolvable combinatorial designs including Resolvable Balanced Incomplete Block Designs, Resolvable Group Divisible Designs, Uniformly Resolvable Designs and Mutually Orthogonal Latin Squares and Rectangles are used to construct optimal solutions to the Social Golfer problem (SGP) and the Social Golfer problem with adjacent group sizes (SGA). An algorithm is presented to find an optimal solution in general, and a complete set of solutions is provided for up to 150 players.
53 pages (includes 24 pages of appendices. Appendix B is supporting information for journal submission. Submitted to Journal of Combinatorial Designs