Using (sub)graphs of small width for solving the Steiner problem

For the Steiner tree problem in networks, we present a practical algorithm that uses the fixed-parameter tractability of the problem with respect to a certain width parameter closely related to pathwidth. The running time of the algorithm is linear in the number of vertices when the pathwidth is constant. Combining this algorithm with our previous techniques, we can already profit from small width in subgraphs of an instance. Integrating this algorithm into our program package for the Steiner problem accelerates the solution process on some groups of instances and leads to a fast solution of some previously unsolved benchmark instances