{"title":"求给定直径边不相交生成树最小总重的渐近最优方法","authors":"E. Kh. Gimadi, A. A. Shtepa","doi":"10.1134/S0005117923070068","DOIUrl":null,"url":null,"abstract":"<p>We consider the intractable problem of finding several edge-disjoint spanning trees of the minimum total weight with a given diameter in complete undirected graph in current paper. The weights of edges of a graph are random variables from several continuous distributions: uniform, biased truncated exponential, biased truncated normal. The approximation algorithm with time complexity <span>\\(\\mathcal{O}\\)</span>(<i>n</i><sup>2</sup>), where <i>n</i> is number of vertices in graph, is proposed for solving this problem. The asymptotic optimality conditions for constructed algorithm is presented for each considered probabilistic distribution.</p>","PeriodicalId":55411,"journal":{"name":"Automation and Remote Control","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Asymptotically Optimal Approach for Finding of the Minimum Total Weight of Edge-Disjoint Spanning Trees with a Given Diameter\",\"authors\":\"E. Kh. Gimadi, A. A. Shtepa\",\"doi\":\"10.1134/S0005117923070068\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We consider the intractable problem of finding several edge-disjoint spanning trees of the minimum total weight with a given diameter in complete undirected graph in current paper. The weights of edges of a graph are random variables from several continuous distributions: uniform, biased truncated exponential, biased truncated normal. The approximation algorithm with time complexity <span>\\\\(\\\\mathcal{O}\\\\)</span>(<i>n</i><sup>2</sup>), where <i>n</i> is number of vertices in graph, is proposed for solving this problem. The asymptotic optimality conditions for constructed algorithm is presented for each considered probabilistic distribution.</p>\",\"PeriodicalId\":55411,\"journal\":{\"name\":\"Automation and Remote Control\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2023-10-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Automation and Remote Control\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0005117923070068\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Automation and Remote Control","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1134/S0005117923070068","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
On Asymptotically Optimal Approach for Finding of the Minimum Total Weight of Edge-Disjoint Spanning Trees with a Given Diameter
We consider the intractable problem of finding several edge-disjoint spanning trees of the minimum total weight with a given diameter in complete undirected graph in current paper. The weights of edges of a graph are random variables from several continuous distributions: uniform, biased truncated exponential, biased truncated normal. The approximation algorithm with time complexity \(\mathcal{O}\)(n2), where n is number of vertices in graph, is proposed for solving this problem. The asymptotic optimality conditions for constructed algorithm is presented for each considered probabilistic distribution.
期刊介绍:
Automation and Remote Control is one of the first journals on control theory. The scope of the journal is control theory problems and applications. The journal publishes reviews, original articles, and short communications (deterministic, stochastic, adaptive, and robust formulations) and its applications (computer control, components and instruments, process control, social and economy control, etc.).