Lower bounds for the relative greedy algorithm for approximating Steiner trees

The Steiner tree problem is to find a shortest subgraph that spans a given set of vertices in a graph. This problem is known to be NP-hard and it is well known that a polynomial time 2-approximation algorithm exists. In 1996 Zelikovsky [11] suggested an approximation algorithm for the Steiner tree problem that is called the relative greedy algorithm. Till today the performance ratio of this algorithm is not known. Zelikovsky provided 1.694 as an upper bound and Gröpl, Hougardy, Nierhoff and Prömel [6] proved that 1.333 is a lower bound. In this paper we improve the lower bound for the performance ratio of the relative greedy algorithm to 1.385.