The relation of Connected Set Cover and Group Steiner Tree

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• 作者：Khaled Elbassioni^a ; ¹ ; ^{elbassio@mpi-inf.mpg.de} ; Slobodan Jeli?^b ; ^{sjelic@mathos.hr} ; ^{sljelic@gmail.com} ; Domagoj Matijevi?^c ; ² ; ^{domagoj@mathos.hr}
• 关键词：Set cover ; Connected set cover ; Weighted connected set cover ; Group Steiner tree ; Node weighted group Steiner tree ; Covering Steiner tree problem
• 刊名：Theoretical Computer Science
• 出版年：2012
• 出版时间：22 June, 2012
• 年：2012
• 卷：438
• 期：Complete
• 页码：96-101
• 全文大小：217 K

文摘

We report that the Connected Set Cover (CSC) problem is just a special case of the Group Steiner Tree (GST) problem. Based on that we obtain the first algorithm for CSC with polylogarithmic approximation guarantee as well as the first approximation algorithms for the weighted version of the problem and the version with requirements. Moreover, we argue that the inapproximability result of GST will carry on to the weighted version of the CSC problem.