约束松弛对最小顶点覆盖问题动态临界现象的影响

IF 1.8 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

EPL Pub Date : 2024-07-24 DOI:10.1209/0295-5075/ad5102

A. Dote and K. Hukushima

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引用次数: 0

摘要

本研究利用马尔可夫链蒙特卡罗模拟，研究了在厄尔多斯-雷尼随机图的最小顶点覆盖（MVC）问题中，约束松弛对动态临界现象的影响。我们之前的研究揭示了基于惩罚函数法的约束松弛降低了临界温度。研究发现，MVC 的动态相关函数与问题大小和约束强度的关系遵循一个普遍的缩放函数。分析表明，松弛时间随着约束条件的松弛而减少。临界振幅的减小比临界指数的减小更明显，这一结果可以从约束松弛导致的系统微观能量障碍的角度来解释。

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Effect of constraint relaxation on dynamic critical phenomena in minimum vertex cover problem

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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来源期刊

EPL 物理-物理：综合

CiteScore

3.30

自引率

5.60%

发文量

332

审稿时长

1.9 months

期刊介绍： General physics – physics of elementary particles and fields – nuclear physics – atomic, molecular and optical physics – classical areas of phenomenology – physics of gases, plasmas and electrical discharges – condensed matter – cross-disciplinary physics and related areas of science and technology. Letters submitted to EPL should contain new results, ideas, concepts, experimental methods, theoretical treatments, including those with application potential and be of broad interest and importance to one or several sections of the physics community. The presentation should satisfy the specialist, yet remain understandable to the researchers in other fields through a suitable, clearly written introduction and conclusion (if appropriate). EPL also publishes Comments on Letters previously published in the Journal.