Practical partitioning-based methods for the Steiner problem

Partitioning is one of the basic ideas for designing efficient algorithms, but on 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.