A Fast Heuristic Algorithm for the Steiner Tree Problem with Uniform Edge Weights

The Steiner tree problem, which asks for a tree of minimum weight that spans all the terminals in the given network, is a challenging NP-hard problem. Applications of the problem can be found in many practical applications in artificial intelligence, network design and so on. In this paper, we study an effective iterative local search (ILS) algorithm for solving this problem in a graph with uniform edge weights. The algorithm uses several strong graph reduction techniques and a novel neighborhood generation method, namely Steiner-edge-vertex swap. We conduct experiments on a wide range of well-known instances and confirm that our algorithm competes favorably with other state-of-the-art algorithms. Further experiments also validate the effectiveness of the proposed techniques.