A Novel Heuristic Algorithm for Solving Euclidean Steiner Tree Problem

The Steiner problem leads to solutions in several scientific and business applications. Computer networks routing and electronic integrated circuits are few examples of it. Assuming some points in the Euclidean plane, we can construct a minimum spanning tree connecting these (terminal) nodes. It is possible to add some extra points (Steiner Points) in order to decrease the length of this tree, which would in turn lead to Euclidean Steiner Minimal Tree (ESMT). The problem is NP-hard, so polynomial-time heuristics are desired. We present a novel heuristic for the Euclidean Steiner tree problem. The algorithm utilizes the straight skeleton of simple polygon to generate candidate Steiner points, and a path heuristic to constructing Steiner minimum tree by using some of the candidate Steiner points in Euclidean plane. We present computational results on the Soukup test problems.