AI-based modeling of resource allocation and load balancing on Cayley graphs

The growing complexity of cloud and multiprocessor systems demands efficient resource allocation and load balancing techniques. This paper proposes a novel artificial intelligence-based approach for modeling these processes over Cayley graphs generated by finite permutation groups. Cayley graphs, due to their recursive structure and symmetry, offer advantages in routing and computational design. A universal algorithm is developed to compute shortest paths on such graphs, achieving linear time complexity <i>O</i>(∣ <i>w</i> ∣) . In parallel, a syntax analysis method for context-free grammars is introduced, which supports compiler development in high-performance environments where parsing tools are unavailable. Graph Neural Networks (GNN) are applied to enhance decision-making accuracy in dynamic allocation. Experimental results reveal new properties in modified bubble-sort Cayley graphs and validate the effectiveness of the proposed models. This work contributes to the development of scalable, intelligent infrastructures for modern data centers and multiprocessor computing.