On better heuristic for euclidean Steiner minimum trees (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Biconnectivity approximations and graph carvings
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
A general approximation technique for constrained forest problems
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
A primal-dual approximation algorithm for generalized Steiner network problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Biconnectivity approximations and graph carvings
Journal of the ACM (JACM)
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
On exact solutions for the rectilinear Steiner tree problem
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Provably good routing tree construction with multi-port terminals
Proceedings of the 1997 international symposium on Physical design
A scaling technique for better network design
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Improved approximation bounds for the group Steiner problem
Proceedings of the conference on Design, automation and test in Europe
Design and Evaluation of a Multi-class Based Multicast Routing Protocol
Information Networking. Towards Ubiquitous Networking and Services
Approximation schemes for steiner forest on planar graphs and graphs of bounded treewidth
Proceedings of the forty-second ACM symposium on Theory of computing
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
Journal of the ACM (JACM)
Improved Approximation Algorithms for Prize-Collecting Steiner Tree and TSP
SIAM Journal on Computing
A simple proof of the planar rectilinear Steiner ratio
Operations Research Letters
Multi-rooted greedy approximation of directed steiner trees with applications
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
On the low-dimensional Steiner minimum tree problem in Hamming metric
Theoretical Computer Science
A Survey of Parallel and Distributed Algorithms for the Steiner Tree Problem
International Journal of Parallel Programming
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For a set S contained in a metric space, a Steiner tree of S is a tree that connects the points in S. Finding a minimum cost Steiner tree is an NP-hard problem in euclidean and rectilinear metrics as well as in graphs. We give an approximation algorithm and show that the worst-case ratio of the cost of our solutions to the optimal cost is better than previously known ratios in graphs, and in rectilinear metric on the plane. Our method offers a trade-off between the running time and the ratio; on one hand it always allows to improve the ratio, on the other it allows to obtain previously known ratios with much greater efficiency. We use properties of optimal rectilinear Steiner trees to obtain significantly better ratio and running time in rectilinear metric.