The computation of nearly minimal Steiner trees in graphs

The computation of a minimal Steiner tree for a general weighted graph is known to be NP-hard. Except for very simple cases, it is thus computationally impracticable to use an algorithm which produces an exact solution. This paper describes a heuristic algorithm which runs in polynomial time and produces a near minimal solution. Experimental results show that the algorithm performs satisfactorily in the rectilinear case. The paper provides an interesting case study of NP-hard problems and of the important technique of heuristic evaluation.