Algorithms for the Prize-Collecting $k$-Steiner Tree Problem

doi:10.26599/TST.2021.9010053

	Algorithms for the Prize-Collecting $k$-Steiner Tree Problem
	Han, Lu 3; Wang, Changjun 2; Xu, Dachuan 1; Zhang, Dongmei 4
刊名	TSINGHUA SCIENCE AND TECHNOLOGY
	2022-10-01
卷号	27 期号:5 页码:785-792
关键词	Steiner trees Costs Approximation algorithms prize-collecting Steiner tree approximation algorithm
ISSN号	1007-0214
DOI	10.26599/TST.2021.9010053
英文摘要	In this paper, we study the prize-collecting $k$-Steiner tree ($\mathsf{PC}k\mathsf{ST}$) problem. We are given a graph $G=(V, E)$ and an integer $k$. The graph is connected and undirected. A vertex $r\in V$ called root and a subset $R\subseteq V$ called terminals are also given. A feasible solution for the $\mathsf{PC}k\mathsf{ST}$ is a tree $F$ rooted at $r$ and connecting at least $k$ vertices in $R$. Excluding a vertex from the tree incurs a penalty cost, and including an edge in the tree incurs an edge cost. We wish to find a feasible solution with minimum total cost. The total cost of a tree $F$ is the sum of the edge costs of the edges in $F$ and the penalty costs of the vertices not in $F$. We present a simple approximation algorithm with the ratio of 5.9672 for the $\mathsf{PC}k\mathsf{ST}$. This algorithm uses the approximation algorithms for the prize-collecting Steiner tree (PCST) problem and the $k$-Steiner tree ($k\mathsf{ST}$) problem as subroutines. Then we propose a primal-dual based approximation algorithm and improve the approximation ratio to 5.
资助项目	National Natural Science Foundation of China[12001523] ; National Natural Science Foundation of China[11971046] ; National Natural Science Foundation of China[12131003] ; National Natural Science Foundation of China[11871081] ; Scientific Research Project of Beijing Municipal Education Commission[KM201910005012] ; Beijing Natural Science Foundation Project[Z200002]
WOS研究方向	Computer Science ; Engineering
语种	英语
出版者	TSINGHUA UNIV PRESS
WOS记录号	WOS:000770606800004
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/60212]
专题	中国科学院数学与系统科学研究院
通讯作者	Xu, Dachuan
作者单位	1.Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China 4.Shandong Jianzhu Univ, Sch Comp Sci & Technol, Jinan 250101, Peoples R China
推荐引用方式 GB/T 7714	Han, Lu,Wang, Changjun,Xu, Dachuan,et al. Algorithms for the Prize-Collecting $k$-Steiner Tree Problem[J]. TSINGHUA SCIENCE AND TECHNOLOGY,2022,27(5):785-792.
APA	Han, Lu,Wang, Changjun,Xu, Dachuan,&Zhang, Dongmei.(2022).Algorithms for the Prize-Collecting $k$-Steiner Tree Problem.TSINGHUA SCIENCE AND TECHNOLOGY,27(5),785-792.
MLA	Han, Lu,et al."Algorithms for the Prize-Collecting $k$-Steiner Tree Problem".TSINGHUA SCIENCE AND TECHNOLOGY 27.5(2022):785-792.