KMS Of Academy of mathematics and systems sciences, CAS
Algorithms for the Prize-Collecting $k$-Steiner Tree Problem | |
Han, Lu1; Wang, Changjun2; Xu, Dachuan3; Zhang, Dongmei4 | |
2022-10-01 | |
发表期刊 | TSINGHUA SCIENCE AND TECHNOLOGY |
ISSN | 1007-0214 |
卷号 | 27期号:5页码:785-792 |
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. |
关键词 | Steiner trees Costs Approximation algorithms prize-collecting Steiner tree approximation algorithm |
DOI | 10.26599/TST.2021.9010053 |
收录类别 | SCI |
语种 | 英语 |
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 |
WOS类目 | Computer Science, Information Systems ; Computer Science, Software Engineering ; Engineering, Electrical & Electronic |
WOS记录号 | WOS:000770606800004 |
出版者 | TSINGHUA UNIV PRESS |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.amss.ac.cn/handle/2S8OKBNM/60213 |
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 Posts & Telecommun, Sch Sci, Beijing 100876, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, 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. |
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