{"title":"NP-Completeness of the minimum edge-ranking spanning tree problem on series-parallel graphs","authors":"A. Arefin, M.A. Kashem Mia","doi":"10.1109/ICCITECHN.2007.4579371","DOIUrl":null,"url":null,"abstract":"The minimum edge-ranking spanning tree (MERST) problem on a graph is to find a spanning tree of G whose edge-ranking needs least number of ranks. Although polynomial-time algorithm to solve the minimum edge-ranking spanning tree problem on series-parallel graphs with bounded degrees has been found, but for the unbounded degrees no polynomial-time algorithm is known. In this paper, we prove that the minimum edge-ranking spanning tree problem on general series-parallel graph is NP-complete.","PeriodicalId":338170,"journal":{"name":"2007 10th international conference on computer and information technology","volume":"81 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2007 10th international conference on computer and information technology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICCITECHN.2007.4579371","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
The minimum edge-ranking spanning tree (MERST) problem on a graph is to find a spanning tree of G whose edge-ranking needs least number of ranks. Although polynomial-time algorithm to solve the minimum edge-ranking spanning tree problem on series-parallel graphs with bounded degrees has been found, but for the unbounded degrees no polynomial-time algorithm is known. In this paper, we prove that the minimum edge-ranking spanning tree problem on general series-parallel graph is NP-complete.
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