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    Rights statement: This is the peer reviewed version of the following article: Rehfeldt D, Koch T, Maher SJ. Reduction techniques for the prize collecting Steiner tree problem and the maximum‐weight connected subgraph problem. Networks. 2018;1–28. https://doi.org/10.1002/net.21857 which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/net.21857 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.

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    Available under license: CC BY-NC: Creative Commons Attribution-NonCommercial 4.0 International License

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

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<mark>Journal publication date</mark>03/2019
<mark>Journal</mark>Networks
Issue number2
Volume73
Number of pages28
Pages (from-to)206-233
Publication StatusPublished
Early online date26/10/18
<mark>Original language</mark>English

Abstract

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.

Bibliographic note

This is the peer reviewed version of the following article: Rehfeldt D, Koch T, Maher SJ. Reduction techniques for the prize collecting Steiner tree problem and the maximum‐weight connected subgraph problem. Networks. 2018;1–28. https://doi.org/10.1002/net.21857 which has been published in final form at https://onlinelibrary.wiley.com/doi/10.1002/net.21857 This article may be used for non-commercial purposes in accordance With Wiley Terms and Conditions for self-archiving.