Social Golfer Problem Revisited

In a golf club, $$n=g*s$$ golfers want to play in g groups of s golfers for w weeks. Does there exist a schedule for each golfer to play no more than once with any other golfer? This simple but overwhelmingly challenging problem, which is called social golfer problem (SGP), has received considerable attention in constraint satisfaction problem (CSP) research as a standard benchmark for symmetry breaking. However, constraint satisfaction approach for solving the SGP has stagnated in terms of larger instance over the last decade. In this article, we improve the existing model of the SGP by introducing more constraints that effectively reduce the search space, particularly for the instances of the specific form. And on this basis, we also provide a search space splitting method to solve the SGP in parallel via data-level parallelism. Our implementation of the presented techniques allows us to attain the solutions for eight instances with maximal number of weeks, in which six of them were open instances for constraint satisfaction approach, and two of them are computed for the first time, and super-linear speedups are observed for all the instances solved in parallel. Besides, we survey the extensive literature on solving the SGP, including the best results they have achieved, and analyse the cause of difficulties in solving the SGP.