Investigating monte-carlo methods on the weak schur problem

Nested Monte-Carlo Search (NMC) and Nested Rollout Policy Adaptation (NRPA) are Monte-Carlo tree search algorithms that have proved their efficiency at solving one-player game problems, such as morpion solitaire or sudoku 16x16, showing that these heuristics could potentially be applied to constraint problems. In the field of Ramsey theory, the weak Schur numberWS(k) is the largest integer n for which their exists a partition into k subsets of the integers [1,n] such that there is no x

Keywords:

• Combinatorics
• Tree traversal
• Partition (number theory)
• Monte Carlo method
• Ramsey theory
• Search algorithm
• Heuristics
• Integer
• Mathematics
• Discrete mathematics
• Upper and lower bounds

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