Tighter Bounds for Graph Steiner Tree Approximation

The classical Steiner tree problem in weighted graphs seeks a minimum weight connected subgraph containing a given subset of the vertices (terminals). We present a new polynomialtime heuristic that achieves a best-known approximation ratio of 1 + ln 3 2 ≈ 1.55 for general graphs, and best-known approximation ratios of ≈ 1.28 for quasi-bipartite graphs (i.e., where no two non-terminals are adjacent) and for complete graphs with edge weights 1 and 2. Our method is considerably simpler and easier to implement than previous approaches. We also prove the first known non-trivial performance bound (1.5 · OPT) for the Iterated 1-Steiner heuristic of Kahng and Robins in quasi-bipartite graphs.