Gasarch, Glenn, and Kruskal have performed a comparison of different computational methods for large subsets of \{1,\dots n\} with no arithmetic progression. Using these methods they found the exact size of the largest such set for n\le 187. Their results include several new bounds for different values of n, found by branch-and-bound algorithms that use linear programming and problem-specific heuristics to bound the size that can be achieved in any branch of the search tree. One heuristic that they found to be particularly effective was the thirds method, in which two shifted copies of a Salem–Spencer set for n are placed in the first and last thirds of a set for 3n.
