Arthur Pratti Dadalto, F. Usberti, M. C. S. Felice
{"title":"最小子图直径问题的逼近性","authors":"Arthur Pratti Dadalto, F. Usberti, M. C. S. Felice","doi":"10.5753/ETC.2018.3169","DOIUrl":null,"url":null,"abstract":"This work addresses the minimum subgraph diameter problem (MSDP) by answering an open question with respect to its approximability. Given a graph with lengths and costs associated to its edges, the MSDP consists in finding a spanning subgraph with total cost limited by a given budget, such that its diameter is minimum. We prove that there is no -approximation algorithm for the MSDP, for any constant , unless P = NP. Our proof is grounded on the non-approximability of the minimum spanning tree diameter problem, proven by Bálint in 2013.","PeriodicalId":315906,"journal":{"name":"Anais do Encontro de Teoria da Computação (ETC)","volume":"3 5","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Approximability of the Minimum Subgraph Diameter Problem\",\"authors\":\"Arthur Pratti Dadalto, F. Usberti, M. C. S. Felice\",\"doi\":\"10.5753/ETC.2018.3169\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work addresses the minimum subgraph diameter problem (MSDP) by answering an open question with respect to its approximability. Given a graph with lengths and costs associated to its edges, the MSDP consists in finding a spanning subgraph with total cost limited by a given budget, such that its diameter is minimum. We prove that there is no -approximation algorithm for the MSDP, for any constant , unless P = NP. Our proof is grounded on the non-approximability of the minimum spanning tree diameter problem, proven by Bálint in 2013.\",\"PeriodicalId\":315906,\"journal\":{\"name\":\"Anais do Encontro de Teoria da Computação (ETC)\",\"volume\":\"3 5\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-07-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Anais do Encontro de Teoria da Computação (ETC)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5753/ETC.2018.3169\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Anais do Encontro de Teoria da Computação (ETC)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5753/ETC.2018.3169","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Approximability of the Minimum Subgraph Diameter Problem
This work addresses the minimum subgraph diameter problem (MSDP) by answering an open question with respect to its approximability. Given a graph with lengths and costs associated to its edges, the MSDP consists in finding a spanning subgraph with total cost limited by a given budget, such that its diameter is minimum. We prove that there is no -approximation algorithm for the MSDP, for any constant , unless P = NP. Our proof is grounded on the non-approximability of the minimum spanning tree diameter problem, proven by Bálint in 2013.
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