A Heuristic Algorithm for Solving Steiner Tree Problem on the Graph

Steiner tree problem on the graph is an NPComplete problem and has no exact solution in polynomial time. Since this problem is practically useful, there are more attentions to heuristic and approximation approaches rather than exact ones. By using heuristic algorithms, the near optimum answers are obtained in polynomial time that this is faster than exact approaches. The goal of Steiner Tree problem is to find a minimum cost tree from the main graph that connects a subset of nodes called terminals. In this article, we have proposed a heuristic algorithm that solves Steiner Tree Problem. It has time complexity of ( ( + log )) that is the number of nodes and is the number of edges. This algorithm finds the near optimum answer and according to the experimental results and the comparisons, it has an appropriate rate in a reasonable time.