A nearly best-possible approximation algorithm for node-weighted Steiner trees
Journal of Algorithms
Approximation algorithms for facility location problems (extended abstract)
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Improved methods for approximating node weighted Steiner trees and connected dominating sets
Information and Computation
Greedy strikes back: improved facility location algorithms
Journal of Algorithms
Approximation algorithms for directed Steiner problems
Journal of Algorithms
Provisioning a virtual private network: a network design problem for multicommodity flow
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Improved Combinatorial Algorithms for the Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Primal-Dual Approximation Algorithms for Metric Facility Location and k-Median Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Building Steiner trees with incomplete global knowledge
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Primal-Dual Algorithms for Connected Facility Location Problems
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
Simpler and better approximation algorithms for network design
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximation via cost sharing: Simpler and better approximation algorithms for network design
Journal of the ACM (JACM)
Combinatorial optimization in system configuration design
Automation and Remote Control
A hybrid VNS for connected facility location
HM'07 Proceedings of the 4th international conference on Hybrid metaheuristics
Dual-Based Local Search for the Connected Facility Location and Related Problems
INFORMS Journal on Computing
Branch-and-Cut-and-Price for Capacitated Connected Facility Location
Journal of Mathematical Modelling and Algorithms
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The Steiner tree problem is defined as follows-given a graph G = (V, E) and a subset X ⊆ V of terminals, compute a minimum cost tree that includes all nodes in X. Furthermore, it is reasonable to assume that the edge costs form a metric. This problem is NP-hard and has been the study of many heuristics and algorithms. We study a generalization of this problem, where there is a "switch" cost in addition to the cost of the edges. Switches are placed at internal nodes of the tree (essentially, we may assume that all non-leaf nodes of the Steiner tree have a switch). The cost for placing a switch may vary from node to node. A restricted version of this problem, where the terminal set X cannot be connected to each other directly but only via the Steiner nodes V \ X, is referred to as the Steiner Tree-Star problem. The General Steiner Tree-Star problem does not require the terminal set and Steiner node set to be disjoint. This generalized problem can be reduced to the node weighted Steiner tree problem, for which algorithms with performance guarantees of Θ(ln n) are known. However, such approach does not make use of the fact that the edge costs form a metric. In this paper we derive approximation algorithms with small constant factors for this problem. We show two different polynomial time algorithms with approximation factors of 5.16 and 5.