{"title":"序列并行图上最小边排序生成树问题的np -完备性","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":"{\"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}","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}
NP-Completeness of the minimum edge-ranking spanning tree problem on series-parallel graphs
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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