基于密度依赖的骨干构造与强化学习补全实现代数连通性最大化
Toward Maximizing Algebraic Connectivity via Density-Dependent Backbone Construction and Reinforcement Learning Completion
AI总结：
该研究针对固定顶点与边数下最大化图代数连通性的网络设计问题，提出密度依赖的骨干构造结合强化学习补全的方法，实验显示其性能优于现有方法，为可扩展网络设计提供了新策略。
摘要：
本文研究在固定顶点数和边数下构造具有最大代数连通性的图拓扑这一开放网络设计问题。提出一种密度依赖方法，将设计任务分解为两个阶段：高质量低成本的结构骨干构造阶段与强化学习补全阶段。该方法基于密度选择骨干，在稠密区域使用完全多部图，在低至中等密度区域使用Cayley图，随后通过基于学习的过程优化剩余边。数值结果表明，所提方法在代数连通性高的同时具备良好的运行时可扩展性，优于现有方法，这些结果为可扩展网络设计的优先结构族策略提供了支持。
英文摘要：
This paper studies an open network design problem of constructing graph topologies with maximum algebraic connectivity under fixed numbers of vertices and edges. A density-dependent approach is proposed that decomposes the design task into two stages: a high-quality, low-cost structural backbone construction and a reinforcement learning completion stage. The method selects the backbone based on density, using complete multipartite graphs in dense regimes and Cayley graphs in low-to-intermediate regimes, and then refines the remaining edges through a learning-based procedure. Numerical results show that the proposed method achieves high algebraic connectivity with favorable runtime scalability, outperforming existing methods. These results support a structural-family-first strategy for scalable network design.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
