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We present a new exact algorithm for the Steiner tree problem inedge-weighted graphs. Our algorithm improves the classical dynamic programmingapproach by Dreyfus and Wagner. We achieve a significantly better practicalperformance via pruning and future costs, a generalization of a well-knownconcept to speed up shortest path computations. Our algorithm matches the bestknown worst-case run time and has a fast, often superior, practicalperformance: on some large instances originating from VLSI design, previousbest run times are improved upon by orders of magnitudes. We are also able tosolve larger instances of the $d$-dimensional rectilinear Steiner tree problemfor $d \in \{3, 4, 5\}$, whose Hanan grids contain up to several millions ofedges.

Dijkstra meets Steiner: a fast exact goal-oriented Steiner tree algorithm