Reduction techniques for the prize collecting Steiner tree problem and the maximum-weight connected subgraph problem

This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record The concept of reduction has frequently distinguished itself as a pivotal ingredient of exact solving approaches for the Steiner tree problem in graphs. In this article we broaden the focus and consider reduction techniques for three Steiner problem variants that have been extensively discussed in the literature and entail various practical applications: The prize-collecting Steiner tree problem, the rooted prize-collecting Steiner tree problem and the maximum-weight connected subgraph problem. By introducing and subsequently deploying numerous new reduction methods, we are able to drastically decrease the size of a large number of benchmark instances, already solving more than 90% of them to optimality. Furthermore, we demonstrate the impact of these techniques on exact solving, using the example of the state-of-the-art Steiner problem solver SCIP-JACK.Bundesministerium für Wirtschaft und Energie,. Deutsche Forschungsgemeinschaft. European Cooperation in Science and Technology. German Federal Ministry of Education and Researc