AI 中文总结
该研究针对匹配、旅行商等组合优化问题，提出将其转化为排列模型并置于巨正则系综的框架，利用化学势放宽约束，找到解析解作为多项式时间算法，补充现有方法并揭示新联系。
AI 中文摘要
我们引入一个通用框架来解决一类组合优化问题，包括匹配问题、旅行商问题以及最小权重k因子问题。通过将这些问题重新表述为排列模型，我们把优化任务转化为巨正则系综，利用化学势来放宽严格的拓扑约束。找到的解析解可作为多项式时间算法，为任意k和链路权重分布计算近似最小成本。我们的框架补充了现有方法，并揭示了组合优化与无序系统统计物理之间的新联系。
英文摘要
We introduce a general framework to solve a class of combinatorial opti- mization problems, including the matching problem, the Traveling Salesman Problem, and also the minimum weight k-factor problem. By reformulating these problems as an arrangement model, we recast the optimization task into a grand-canonical ensemble, where chemical potentials are used to re- lax strict topological constraints. The analytical solution found can serve as a polynomial-time algorithm to compute an approximate minimum cost for arbitrary k and link-weight distributions. Our framework is complementary to existing approaches and reveals new connections between combinatorial optimization and the statistical physics of disordered systems.
Comments25 pages, 7 figures
Journal refVolume 207,2026,118012,ISSN 0960-0779
DOI：10.1016/j.chaos.2026.118012
