Algorithms for the Prize-Collecting $k$-Steiner Tree Problem
Han, Lu1; Wang, Changjun2; Xu, Dachuan3; Zhang, Dongmei4
AbstractIn 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.
KeywordSteiner trees Costs Approximation algorithms prize-collecting Steiner tree approximation algorithm
Indexed BySCI
Funding ProjectNational 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 Research AreaComputer Science ; Engineering
WOS SubjectComputer Science, Information Systems ; Computer Science, Software Engineering ; Engineering, Electrical & Electronic
WOS IDWOS:000770606800004
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Document Type期刊论文
Corresponding AuthorXu, Dachuan
Affiliation1.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
Recommended Citation
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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