Noname manuscript No. (will be inserted by the editor) An Improved SAT Formulation for the Social Golfer Problem

Abstract The Social Golfer Problem (SGP) is a sports scheduling problem that ex-hibits a lot of symmetry and has recently attracted significant attention. In this paper, we first revisit an existing SAT encoding for the SGP and correct some of its clauses. We then propose a change in the encoding that significantly reduces the number of variables for all instances. We achieve considerable performance improvements when solving many SGP instances with common SAT solvers using local search and complete backtracking. This makes SAT formulations a more promising approach for solving the SGP than previously. Keywords sports scheduling · combinatorial optimization · design theory · finite geometry