TY - GEN

T1 - On the minimum diameter cost-constrained steiner tree problem

AU - Ding, Wei

AU - Xue, Guoliang

PY - 2012

Y1 - 2012

N2 - Given an edge-weighted undirected graph G = (V,E,c,w) where each edge e ∈ E has a cost c(e) ≥ 0 and another weight w(e) ≥ 0, a set S ⊆ V of terminals and a given constant C 0 ≥ 0, the aim is to find a minimum diameter Steiner tree whose all terminals appear as leaves and the cost of tree is bounded by C 0. The diameter of tree refers to the maximum weight of the paths connecting two different leaves in the tree. This problem is called the minimum diameter cost-constrained Steiner tree problem, which is NP-hard even when the topology of the Steiner tree is fixed. In this paper, we deal with the fixed-topology restricted version. We prove the restricted version to be polynomially solvable when the topology is not part of the input and propose a weakly fully polynomial time approximation scheme (weakly FPTAS) when the topology is part of the input, which can find a (1 + ε)-approximation of the restricted version problem for any ε > 0 with specific characteristic.

AB - Given an edge-weighted undirected graph G = (V,E,c,w) where each edge e ∈ E has a cost c(e) ≥ 0 and another weight w(e) ≥ 0, a set S ⊆ V of terminals and a given constant C 0 ≥ 0, the aim is to find a minimum diameter Steiner tree whose all terminals appear as leaves and the cost of tree is bounded by C 0. The diameter of tree refers to the maximum weight of the paths connecting two different leaves in the tree. This problem is called the minimum diameter cost-constrained Steiner tree problem, which is NP-hard even when the topology of the Steiner tree is fixed. In this paper, we deal with the fixed-topology restricted version. We prove the restricted version to be polynomially solvable when the topology is not part of the input and propose a weakly fully polynomial time approximation scheme (weakly FPTAS) when the topology is part of the input, which can find a (1 + ε)-approximation of the restricted version problem for any ε > 0 with specific characteristic.

KW - Minimum diameter

KW - cost-constrained Steiner tree

KW - fixed topology

KW - weakly fully polynomial time approximation scheme

UR - http://www.scopus.com/inward/record.url?scp=84864973156&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84864973156&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-31770-5_4

DO - 10.1007/978-3-642-31770-5_4

M3 - Conference contribution

AN - SCOPUS:84864973156

SN - 9783642317699

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 37

EP - 48

BT - Combinatorial Optimization and Applications - 6th International Conference, COCOA 2012, Proceedings

T2 - 6th Annual International Conference on Combinatorial Optimization and Applications, COCOA 2012

Y2 - 5 August 2012 through 9 August 2012

ER -