{"title":"增加图形以最小化半径","authors":"Joachim Gudmundsson, Y. Sha, Fan Yao","doi":"10.4230/LIPIcs.ISAAC.2021.45","DOIUrl":null,"url":null,"abstract":"We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time (5 / 3 − ϵ )-approximation algorithm, for any ϵ > 0, unless P = NP . We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.","PeriodicalId":11245,"journal":{"name":"Discret. Comput. Geom.","volume":"85 1","pages":"101996"},"PeriodicalIF":0.0000,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Augmenting Graphs to Minimize the Radius\",\"authors\":\"Joachim Gudmundsson, Y. Sha, Fan Yao\",\"doi\":\"10.4230/LIPIcs.ISAAC.2021.45\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time (5 / 3 − ϵ )-approximation algorithm, for any ϵ > 0, unless P = NP . We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.\",\"PeriodicalId\":11245,\"journal\":{\"name\":\"Discret. Comput. Geom.\",\"volume\":\"85 1\",\"pages\":\"101996\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discret. Comput. Geom.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.ISAAC.2021.45\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discret. Comput. Geom.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.ISAAC.2021.45","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We study the problem of augmenting a metric graph by adding k edges while minimizing the radius of the augmented graph. We give a simple 3-approximation algorithm and show that there is no polynomial-time (5 / 3 − ϵ )-approximation algorithm, for any ϵ > 0, unless P = NP . We also give two exact algorithms for the special case when the input graph is a tree, one of which is generalized to handle metric graphs with bounded treewidth.