Zhu
Binhai
10.1007/978-3-319-03780-6_6
doi
approximation ratio
problem
Clustered Steiner tree problem
2013-01-01
ratio
metric graphs
Steiner minimum tree problem
false
graph
inter-cluster tree
chapters
2013
We investigate the Clustered Steiner tree problem on metric graphs, which is a variant of Steiner minimum tree problem. The required vertices are partitioned into clusters, and in a feasible clustered Steiner tree, the subtrees spanning two different clusters must be disjoint. In this paper, we show that the problem remains NP-hard even if the topologies of all clusters and the inter-cluster tree are given. We propose a (ρ + 2)-approximation algorithm for the general case, in which ρ is the approximation ratio for the Steiner tree problem. When the topologies for all clusters are given, we show a (ρ + 1)-approximation algorithm. We also discuss the Steiner ratio for this problem. We show the ratio is lower and upper bounded by three and four, respectively.
paper
chapter
Steiner ratio
general case
2022-01-01T19:11
variants
https://scigraph.springernature.com/explorer/license/
Steiner tree problem
vertices
subtrees
https://doi.org/10.1007/978-3-319-03780-6_6
On the Clustered Steiner Tree Problem
trees
tree problem
minimum tree problem
clusters
algorithm
60-71
disjoint
topology
Steiner tree
en
NP
different clusters
cases
Peter
Widmayer
Numerical and Computational Mathematics
Xu
Yinfeng
Bang Ye
Wu
pub.1047233793
dimensions_id
National Chung Cheng University, 621, ChiaYi, Taiwan, R.O.C.
National Chung Cheng University, 621, ChiaYi, Taiwan, R.O.C.
Combinatorial Optimization and Applications
978-3-319-03780-6
978-3-319-03779-0
Springer Nature
Springer Nature - SN SciGraph project
Mathematical Sciences