Constrained Goal-directed Planar Graph Generation with Grammar-based Reinforcement Learning

Abstract:Planar graphs are central to applications across science and engineering, yet existing generators provide limited support for goal-directed generation under hard structural and geometric feasibility constraints. We propose a dataset-free method for generating planar graph embeddings by combining parametric graph grammars with safe reinforcement learning to optimize generic task-specific objectives while satisfying constraints during construction. We formulate the generation process as a constrained Markov decision process, where the graph grammar defines the state and action spaces. We further introduce an action projection that maps sampled actions toward state-dependent safe sets, improving constraint satisfaction during training. In contrast to classical graph generators and deep generative models, which typically offer limited goal-directed control or rely on weak constraint satisfaction, our method constructs feasible planar graph embeddings directly during generation. We also introduce a benchmark suite for constrained and goal-directed planar graph generation, together with classical and deep generative baselines. Across all benchmark tasks, our method consistently outperforms baselines while satisfying the formulated constraints.

Machine Learning (cs.LG)

arXiv:2610.06244 [cs.LG]

(or arXiv:2610.06244v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.06244 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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