Algorithms for the Prize-Collecting $k$-Steiner Tree Problem
文献类型：期刊论文
| 作者 | Han, Lu4; Wang, Changjun3; Xu, Dachuan2; Zhang, Dongmei1 |
| 刊名 | TSINGHUA SCIENCE AND TECHNOLOGY
 |
| 出版日期 | 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 |
| WOS记录号 | WOS:000770606800004 |
| 出版者 | TSINGHUA UNIV PRESS |
| 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.Shandong Jianzhu Univ, Sch Comp Sci & Technol, Jinan 250101, Peoples R China 2.Beijing Univ Technol, Beijing Inst Sci & Engn Comp, Beijing 100124, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Beijing Univ Posts & Telecommun, Sch Sci, Beijing 100876, 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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