The steiner problem with edge lengths 1 and 2,
Information Processing Letters
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
A General Approximation Technique for Constrained Forest Problems
SIAM Journal on Computing
Spanning Trees---Short or Small
SIAM Journal on Discrete Mathematics
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
A 2.5-factor approximation algorithm for the k-MST problem
Information Processing Letters
New Approximation Guarantees for Minimum-Weight k-Trees and Prize-Collecting Salesmen
SIAM Journal on Computing
Approximation schemes for minimum latency problems
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A constant-factor approximation algorithm for the k-MST problem
Journal of Computer and System Sciences
A 2 + ε approximation algorithm for the k-MST problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
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
A 3-approximation for the minimum tree spanning k vertices
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Primal-dual schema based approximation algorithms
Theoretical aspects of computer science
The Minimum Latency Problem Is NP-Hard for Weighted Trees
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Primal-Dual Schema Based Approximation Algorithms
Theoretical Aspects of Computer Science, Advanced Lectures [First Summer School on Theoretical Aspects of Computer Science, Tehran, Iran, July 2000]
Obtaining optimal k-cardinality trees fast
Journal of Experimental Algorithmics (JEA)
Approximating fault-tolerant group-Steiner problems
Theoretical Computer Science
Euclidean prize-collecting steiner forest
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Prize-collecting steiner networks via iterative rounding
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Prize-collecting Steiner problems on planar graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Prize-Collecting steiner network problems
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Prize-collecting steiner network problems
ACM Transactions on Algorithms (TALG)
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We consider the problem of computing the minimum-cost tree spanning at least k vertices in an undirected graph. Garg [10] gave two approximation algorithms for this problem. We show that Garg's algorithms can be explained simply with ideas introduced by Jain and Vazirani for the metric uncapacitated facility location and k-median problems [15], in particular via a Lagrangean relaxation technique together with the primal-dual method for approximation algorithms. We also derive a constant-factor approximation algorithm for the k-Steiner tree problem using these ideas, and point out the common features of these problems that allow them to be solved with similar techniques.