Combinatorial solutions to the Social Golfer Problem and Social Golfer Problem with Adjacent Group Sizes

TL;DR

This paper introduces combinatorial design-based methods and algorithms to find optimal solutions for the Social Golfer Problem and its variant with adjacent group sizes, achieving solutions for up to 150 players.

Contribution

It presents a novel approach using resolvable combinatorial designs and an algorithm to find optimal solutions for SGP and SGA, including a complete set for up to 150 players.

Findings

Optimal solutions constructed using combinatorial designs.

Algorithm successfully finds solutions for up to 150 players.

Complete solution sets provided for the problems.

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.