AI 中文总结
针对经典VLSI路由问题，通过Prim-Dijkstra算法，证明弱NP完全性，推导成本-半径权衡，构建多模式求解器HP-RCRST，在开发实例上表现出色，重新开启被忽视问题，展现大语言模型对算法研究的推动作用。
AI 中文摘要
大语言模型可能使精确但被搁置的算法问题得以重新探讨，并为基础问题开辟新途径。我们通过Prim-Dijkstra路由（一个经典的VLSI问题，尽管经过数十年实践，其仅终端曼哈顿复杂度仍未解决）来证明这种可能性。我们证明了弱NP完全性，推导了具有平衡(2,2)保证的连续成本-半径权衡，并构建了基于高度划分的多模式求解器HP-RCRST。在28个开发实例上，其更强模式在23个实例上帕累托优于已发表方法的联合，在5个实例上持平。该案例展示了相互冲突的猜想、反例、形式检查和实现如何能重新开启被忽视的问题。代码和可重复性材料可在指定网址获取。
英文摘要
Large language models may make precise but dormant algorithmic problems practical to revisit, and may expose new paths toward fundamental ones. We demonstrate this possibility through Prim-Dijkstra routing, a classic VLSI problem whose terminal-only Manhattan complexity remained open despite decades of practical work. We prove weak NP-completeness, derive a continuous cost-radius tradeoff with a balanced (2,2) guarantee, and build HP-RCRST, a height-partition-based multi-mode solver. On 28 development instances, its stronger modes Pareto-dominate the published-method union on 23 and tie on five. The case shows how conflicting conjectures, counterexamples, formal checks, and implementation can reopen neglected questions. Code and reproducibility materials are available at https://github.com/CODA-Team/hp-rcrst.
Comments23 pages, 6 figures. Code and reproducibility materials: https://github.com/CODA-Team/hp-rcrst
