{"title":"Effect of constraint relaxation on dynamic critical phenomena in minimum vertex cover problem","authors":"A. Dote and K. Hukushima","doi":"10.1209/0295-5075/ad5102","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":11738,"journal":{"name":"EPL","volume":null,"pages":null},"PeriodicalIF":1.8000,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"EPL","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1209/0295-5075/ad5102","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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