On the clustered Steiner tree problem
Bang Ye Wu () and
Chen-Wan Lin
Additional contact information
Bang Ye Wu: National Chung Cheng University
Chen-Wan Lin: National Chung Cheng University
Journal of Combinatorial Optimization, 2015, vol. 30, issue 2, No 11, 370-386
Abstract:
Abstract We investigate the Clustered Steiner tree problem on metric graphs, which is a variant of the Steiner minimum tree problem. In this problem, the required vertices are partitioned into clusters, and the subtrees spanning different clusters must be disjoint in a feasible clustered Steiner tree. In this paper, it is shown that the problem is NP-hard even if the inter-cluster tree and all the local topologies are given, where a local topology specifies the tree structure of required vertices in the same cluster. We show that the Steiner ratio of this problem is lower and upper bounded by three and four, respectively. We also propose a $$(\rho +2)$$ ( ρ + 2 ) -approximation algorithm, where $$\rho $$ ρ is the approximation ratio for the Steiner minimum tree problem, and the approximation ratio can be improved to $$\rho +1$$ ρ + 1 if the local topologies are given. Two variants of this problem are also studied. When the goal is to minimize the inter-cluster cost and ignore the cost of local trees, the problem can be solved in polynomial time. But it is NP-hard if we ask for the minimum cost of local trees among all solutions with minimum inter-cluster cost.
Keywords: Approximation algorithm; Steiner tree; NP-hard; Graph theory (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)
Downloads: (external link)
http://link.springer.com/10.1007/s10878-014-9772-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:spr:jcomop:v:30:y:2015:i:2:d:10.1007_s10878-014-9772-7
Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878
DOI: 10.1007/s10878-014-9772-7
Access Statistics for this article
Journal of Combinatorial Optimization is currently edited by Thai, My T.
More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().