Implications, conflicts, and reductions for Steiner trees

The Steiner tree problem in graphs (SPG) is one of the most studied problems in combinatorial optimization. In the last 10 years, there have been significant advances concerning approximation and complexity of the SPG. However, the state of the art in (practical) exact solution of the SPG has remained largely unchallenged for almost 20 years. While the DIMACS Challenge 2014 and the PACE Challenge 2018 brought renewed interest into Steiner tree problems, even the best new SPG solvers cannot match the state of the art on the vast majority of benchmark instances. The following article seeks to once again advance exact SPG solution. The article is based on a combination of three concepts: Implications, conflicts, and reductions. As a result, various new SPG techniques are conceived. Notably, several of the resulting techniques are (provably) stronger than well-known methods from the literature, used in exact SPG algorithms. Finally, by integrating the new methods into a branch-and-cut algorithm we obtain an exact SPG solver that is not only competitive with, but even outperforms the current state of the art on a large collection of benchmark sets. Furthermore, we can solve several instances for the first time to optimality.



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