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

  title={Dijkstra meets Steiner: a fast exact goal-oriented Steiner tree algorithm},
  author={Stefan Hougardy and Jannik Silvanus and Jens Vygen},
  journal={Mathematical Programming Computation},
We present a new exact algorithm for the Steiner tree problem in edge-weighted graphs. Our algorithm improves the classical dynamic programming approach by Dreyfus and Wagner. We achieve a significantly better practical performance via pruning and future costs, a generalization of a well-known concept to speed up shortest path computations. Our algorithm matches the best known worst-case run time and has a fast, often superior, practical performance: on some large instances originating from… 

A robust and scalable algorithm for the Steiner problem in graphs

The main elements are a multistart algorithm coupled with aggressive combination of elite solutions, both leveraging recently-proposed fast local searches, and a fast implementation of a well-known dual ascent algorithm that makes the heuristics more robust.