A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Computing vertex connectivity: new bounds from old techniques
Journal of Algorithms
Improved algorithms for the Steiner problem in networks
Discrete Applied Mathematics - Special issue on the combinatorial optimization symposium
Extending Reduction Techniques for the Steiner Tree Problem
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Approaches to the Steiner Problem in Networks
Algorithmics of Large and Complex Networks
Optimal edge deletions for signed graph balancing
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Separator-based data reduction for signed graph balancing
Journal of Combinatorial Optimization
Dealing with large hidden constants: engineering a planar steiner tree PTAS
Journal of Experimental Algorithmics (JEA)
Improved steiner tree algorithms for bounded treewidth
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
Improved Steiner tree algorithms for bounded treewidth
Journal of Discrete Algorithms
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Partitioning is one of the basic ideas for designing efficient algorithms, but on $\mathcal{NP}$-hard problems like the Steiner problem, straightforward application of the classical partitioning-based paradigms rarely leads to empirically successful algorithms. In this paper, we present two approaches to the Steiner problem based on partitioning. The first uses the fixed-parameter tractability of the problem with respect to a certain width parameter closely related to path-width. The second approach is based on vertex separators and is new in the sense that it uses partitioning to design reduction methods. Integrating these methods into our program package for the Steiner problem accelerates the solution process on many groups of instances and leads to a fast solution of some previously unsolved benchmark instances.