Improved algorithms for the Steiner problem in networks
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Approximation Hardness of the Steiner Tree Problem on Graphs
SWAT '02 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory
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
A Hybrid GRASP with Perturbations for the Steiner Problem in Graphs
INFORMS Journal on Computing
Tighter Bounds for Graph Steiner Tree Approximation
SIAM Journal on Discrete Mathematics
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Journal of Experimental Algorithmics (JEA)
Maintaining dynamic minimum spanning trees: An experimental study
Discrete Applied Mathematics
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
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We present efficient algorithms that implement four local searches for the Steiner problem in graphs: vertex insertion, vertex elimination, key-path exchange, and key-vertex elimination. In each case, we show how to find an improving solution (or prove that none exists in the neighborhood) in O(m log n) time on graphs with n vertices and m edges. Many of the techniques and data structures we use are relevant in the study of dynamic graphs in general, beyond Steiner trees. Besides the theoretical interest, our results have practical impact: These local searches have been shown to find good-quality solutions in practice, but high running times limited their applicability.