{"title":"方形(0,1)矩阵的最优着色算法","authors":"I. V. Olemskoy, O. S. Firyulina","doi":"10.21638/11701/spbu10.2023.108","DOIUrl":null,"url":null,"abstract":"The paper proposes an algorithm for solving the configuration-optimization coloring problem for square (0,1)-matrices, which is based on the method of selection their structural features. The algorithm belongs to the method's of backtracking, however, the construction of the optimal solution is carried out among the options that provide a certain configuration, due to which the size of the search tree is significantly reduced. A detailed scheme of its operation is given, and the effectiveness of the solution is demonstrated by the example of calculating the chromatic number of a specific (0,1)-matrix.","PeriodicalId":43738,"journal":{"name":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","volume":"136 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Algorithm for optimal coloring of square (0,1)-matrices\",\"authors\":\"I. V. Olemskoy, O. S. Firyulina\",\"doi\":\"10.21638/11701/spbu10.2023.108\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper proposes an algorithm for solving the configuration-optimization coloring problem for square (0,1)-matrices, which is based on the method of selection their structural features. The algorithm belongs to the method's of backtracking, however, the construction of the optimal solution is carried out among the options that provide a certain configuration, due to which the size of the search tree is significantly reduced. A detailed scheme of its operation is given, and the effectiveness of the solution is demonstrated by the example of calculating the chromatic number of a specific (0,1)-matrix.\",\"PeriodicalId\":43738,\"journal\":{\"name\":\"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya\",\"volume\":\"136 1\",\"pages\":\"\"},\"PeriodicalIF\":0.3000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.21638/11701/spbu10.2023.108\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.21638/11701/spbu10.2023.108","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Algorithm for optimal coloring of square (0,1)-matrices
The paper proposes an algorithm for solving the configuration-optimization coloring problem for square (0,1)-matrices, which is based on the method of selection their structural features. The algorithm belongs to the method's of backtracking, however, the construction of the optimal solution is carried out among the options that provide a certain configuration, due to which the size of the search tree is significantly reduced. A detailed scheme of its operation is given, and the effectiveness of the solution is demonstrated by the example of calculating the chromatic number of a specific (0,1)-matrix.
期刊介绍:
The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.