{"title":"论大型集群选择问题的复杂性","authors":"A. V. Pyatkin","doi":"10.1134/S1990478924020121","DOIUrl":null,"url":null,"abstract":"<p> The paper considers the following problem. Given a set of Euclidean vectors, find several\nclusters with a restriction on the maximum scatter of each cluster so that the size of the minimum\ncluster would be maximum. Here the scatter is the sum of squared distances from the cluster\nelements to its centroid. The NP-hardness of this problem is proved in the case where the\ndimension of the space is part of the input.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 2","pages":"312 - 315"},"PeriodicalIF":0.5800,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Complexity of the Problem of Choice\\nof Large Clusters\",\"authors\":\"A. V. Pyatkin\",\"doi\":\"10.1134/S1990478924020121\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> The paper considers the following problem. Given a set of Euclidean vectors, find several\\nclusters with a restriction on the maximum scatter of each cluster so that the size of the minimum\\ncluster would be maximum. Here the scatter is the sum of squared distances from the cluster\\nelements to its centroid. The NP-hardness of this problem is proved in the case where the\\ndimension of the space is part of the input.\\n</p>\",\"PeriodicalId\":607,\"journal\":{\"name\":\"Journal of Applied and Industrial Mathematics\",\"volume\":\"18 2\",\"pages\":\"312 - 315\"},\"PeriodicalIF\":0.5800,\"publicationDate\":\"2024-08-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Industrial Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1990478924020121\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Engineering\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924020121","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
On the Complexity of the Problem of Choice
of Large Clusters
The paper considers the following problem. Given a set of Euclidean vectors, find several
clusters with a restriction on the maximum scatter of each cluster so that the size of the minimum
cluster would be maximum. Here the scatter is the sum of squared distances from the cluster
elements to its centroid. The NP-hardness of this problem is proved in the case where the
dimension of the space is part of the input.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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