Survivable networks, linear programming relaxations and the parsimonious property
Mathematical Programming: Series A and B
The Steiner tree problem I: formulations, compositions and extension of facets
Mathematical Programming: Series A and B
On the bidirected cut relaxation for the metric Steiner tree problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Improved Steiner tree approximation in graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A comparison of Steiner tree relaxations
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Improved algorithms for the Steiner problem in networks
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
On the Implementation of MST-Based Heuristics for the Steiner Problem in Graphs
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Improved approximations for tour and tree covers
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Primal-dual approaches to the Steiner problem
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Extending Reduction Techniques for the Steiner Tree Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Spanning trees in hypergraphs with applications to steiner trees
Spanning trees in hypergraphs with applications to steiner trees
Fourier meets möbius: fast subset convolution
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Dynamic Programming for Minimum Steiner Trees
Theory of Computing Systems
Improving linear programming approaches for the steiner tree problem
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
New geometry-inspired relaxations and algorithms for the metric steiner tree problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Practical partitioning-based methods for the steiner problem
WEA'06 Proceedings of the 5th international conference on Experimental Algorithms
On Steiner trees and minimum spanning trees in hypergraphs
Operations Research Letters
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The Steiner problem in networks is the problem of connecting a set of required vertices in a weighted graph at minimum cost. This is a classical ${\mathcal {NP}}$-hard problem and a fundamental problem in network design with many practical applications. We approach this problem by various means: Relaxations, which relax the feasibility constraints, to get close to an optimal solution; heuristics to find good, but not necessarily optimal solutions; and reductions to simplify problem instances without abandoning the optimal solution. We have integrated these components into an exact algorithm that has achieved outstanding results in practice. In this article, we first provide a brief overview on the main algorithmic developments related to our work on this problem, citing our and others' (already published) works. Then we focus on some central concepts, presenting detailed results on selected topics that offer special insight and potential for further improvement.