{"title":"On minimum vertex bisection of random d-regular graphs","authors":"Josep Díaz , Öznur Yaşar Diner , Maria Serna , Oriol Serra","doi":"10.1016/j.jcss.2024.103550","DOIUrl":null,"url":null,"abstract":"<div><p>Minimum vertex bisection is a graph partitioning problem in which the aim is to find a partition of the vertices into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. In this work we are interested in providing asymptotically almost surely upper bounds on the minimum vertex bisection of random <em>d</em>-regular graphs, for constant values of <em>d</em>. Our approach is based on analyzing a greedy algorithm by using the differential equation method. In this way, we obtain the first known non-trivial upper bounds for the vertex bisection number in random regular graphs. The numerical approximations of these theoretical bounds are compared with the emprical ones, and with the lower bounds from Kolesnik and Wormald (2014) <span>[30]</span>.</p></div>","PeriodicalId":50224,"journal":{"name":"Journal of Computer and System Sciences","volume":"144 ","pages":"Article 103550"},"PeriodicalIF":1.1000,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S002200002400045X/pdfft?md5=5ad9b857ac0144723c133211748957a5&pid=1-s2.0-S002200002400045X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computer and System Sciences","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S002200002400045X","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"BUSINESS, FINANCE","Score":null,"Total":0}
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Abstract
Minimum vertex bisection is a graph partitioning problem in which the aim is to find a partition of the vertices into two equal parts that minimizes the number of vertices in one partition set that have a neighbor in the other set. In this work we are interested in providing asymptotically almost surely upper bounds on the minimum vertex bisection of random d-regular graphs, for constant values of d. Our approach is based on analyzing a greedy algorithm by using the differential equation method. In this way, we obtain the first known non-trivial upper bounds for the vertex bisection number in random regular graphs. The numerical approximations of these theoretical bounds are compared with the emprical ones, and with the lower bounds from Kolesnik and Wormald (2014) [30].
最小顶点分割是一个图分割问题，其目的是将顶点分成相等的两部分，使一个分割集中与另一个分割集中有邻居的顶点数量最小。在这项研究中，我们感兴趣的是在 d 值不变的情况下，为随机 d 不规则图的最小顶点分割提供近似几乎肯定的上界。通过这种方法，我们首次获得了随机规则图中顶点分叉数的非微观上界。我们将这些理论边界的数值近似值与实际边界以及 Kolesnik 和 Wormald（2014）[30] 的下限进行了比较。
期刊介绍：
The Journal of Computer and System Sciences publishes original research papers in computer science and related subjects in system science, with attention to the relevant mathematical theory. Applications-oriented papers may also be accepted and they are expected to contain deep analytic evaluation of the proposed solutions.
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• Complexity theory
• Algorithmic Complexity
• Parallel & distributed computing
• Computer networks
• Neural networks
• Computational learning theory
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• Computer modeling of complex systems
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