约束松弛对最小顶点覆盖问题中动态临界现象的影响
Effect of constraint relaxation on dynamic critical phenomena in minimum vertex cover problem
AI总结：
本研究利用马尔可夫链蒙特卡罗模拟发现，在Erdős-Rényi随机图的MVC问题中，约束松弛使松弛时间减少，且动力学关联函数遵循通用标度函数，临界振幅的减少比临界指数更显著。
摘要：
使用马尔可夫链蒙特卡罗模拟，研究了基于惩罚函数方法的约束松弛对Erdős-Rényi随机图上Minimum Vertex Cover (MVC)问题中动态临界现象的影响。继我们先前工作揭示了约束松弛会降低临界温度之后，本研究重点研究松弛时间沿其相边界的临界性质。研究发现，MVC的动力学关联函数随问题规模和约束强度遵循一个通用标度函数。分析表明，随着约束松弛，松弛时间减少。这种减少在临界振幅上比在临界指数上更为显著，该结果根据约束松弛引起的系统微观能量势垒进行了解释。
英文摘要：
The effects of constraint relaxation on dynamic critical phenomena in the Minimum Vertex Cover (MVC) problem on Erdős-Rényi random graphs are investigated using Markov chain Monte Carlo simulations. Following our previous work that revealed the reduction of the critical temperature by constraint relaxation based on the penalty function method, this study focuses on investigating the critical properties of the relaxation time along its phase boundary. It is found that the dynamical correlation function of MVC with respect to the problem size and the constraint strength follows a universal scaling function. The analysis shows that the relaxation time decreases as the constraints are relaxed. This decrease is more pronounced for the critical amplitude than for the critical exponent, and this result is interpreted in terms of the system's microscopic energy barriers due to the constraint relaxation.
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