Efficient Steiner tree construction based on spanning graphs

The Steiner Minimal Tree (SMT) problem is a very important problem in very large scale integrated computer-aided design. Given n points on a plane, an SMT connects these points through some extra points (called Steiner points) to achieve a minimal total length. Even though there exist many heuristic algorithms for this problem, they have either poor performances or expensive running time. This paper records an implementation of an efficient SMT algorithm that has a worst case running time of O(nlogn) and a performance close to that of the Iterated 1-Steiner algorithm. The algorithm efficiently combines Borah et al.'s edge substitute concept with Zhou et al.'s spanning graph. Extensive experimental studies are conducted to compare it with other programs.