{"title":"Toward systematic generation of 3COL instances based on minimal unsolvable structures","authors":"Kazunori Mizuno, Seiichi Nishihara","doi":"10.1002/ecjc.20359","DOIUrl":null,"url":null,"abstract":"<p>In this paper, the authors propose a method of systematically generating 3-colorable (3COL) graph instances for which a great deal of time and effort are required to obtain a solution (or to determine solvability). This method, which differs from the conventional approach of selecting hard instances from among randomly generated instances, aims to reliably generate hard problems by repeatedly embedding 3COL minimal unsolvable structures in the initial graph. The generated instances conform to various conditions of problems for which the solution searches that had been identified conventionally are extremely difficult. Also, the authors use several solution search algorithms to experimentally verify that the required effort is an exponential order of the number of vertices. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(12): 27–35, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20359</p>","PeriodicalId":100407,"journal":{"name":"Electronics and Communications in Japan (Part III: Fundamental Electronic Science)","volume":"90 12","pages":"27-35"},"PeriodicalIF":0.0000,"publicationDate":"2007-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/ecjc.20359","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronics and Communications in Japan (Part III: Fundamental Electronic Science)","FirstCategoryId":"1085","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/ecjc.20359","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, the authors propose a method of systematically generating 3-colorable (3COL) graph instances for which a great deal of time and effort are required to obtain a solution (or to determine solvability). This method, which differs from the conventional approach of selecting hard instances from among randomly generated instances, aims to reliably generate hard problems by repeatedly embedding 3COL minimal unsolvable structures in the initial graph. The generated instances conform to various conditions of problems for which the solution searches that had been identified conventionally are extremely difficult. Also, the authors use several solution search algorithms to experimentally verify that the required effort is an exponential order of the number of vertices. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(12): 27–35, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20359
基于最小不可解结构的3COL实例的系统生成
在本文中，作者提出了一种系统生成3-可着色（3COL）图实例的方法，对于该图实例，需要大量的时间和精力来获得解（或确定可解性）。该方法不同于从随机生成的实例中选择硬实例的传统方法，旨在通过在初始图中重复嵌入3COL最小不可解结构来可靠地生成硬问题。生成的实例符合问题的各种条件，对于这些条件，传统上确定的解决方案搜索是极其困难的。此外，作者使用了几种解决方案搜索算法来实验验证所需的努力是顶点数量的指数级。©2007 Wiley Periodicals，股份有限公司Electron Comm Jpn Pt 3，90（12）：27-352007；在线发表于Wiley InterScience（www.InterScience.Wiley.com）。DOI 10.1002/ecjc.20359
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