Geometry-Aware MCTS for Extremal Problems in Combinatorial Geometry
We study certain extremal problems in combinatorial geometry that ask about configurations of points in an $n \times n$ grid that satisfy strict, global geometric constraints. Classical exact solvers suffer from combinatorial explosion for these types of problems, and standard reinforcement learning and transformer-based models struggle with the sparse reward "validity cliff" and quadratic token-consumption limits. To overcome these bottlenecks, we propose a Geometry-Aware Monte Carlo Tree Search (MCTS) framework. Our approach strictly enforces geometric constraints through incremental updates to the feasible action space. For constraints about collections of collinear points, like those ...
| Authors | Luoning Zhang, Xu Zhuang, Tianhao Wang et al. |
|---|---|
| Primary category | cs.AI |
| Published | 24 June 2026 |
| Last updated at source | 24 June 2026 |
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