On the approximability of the steiner tree problem

Abstract

We show that it is not possible to approximate the minimum Steiner tree problem within (formula presented) unless co−RP = NP. This improves the currently best known lower bound by about a factor of 3. The reduction is from Håstad’s nonapproximability result for maximum satisfiability of linear equation modulo 2. The improvement on the nonapproximability ratio is mainly based on the fact that our reduction does not use variable gadgets. This idea was introduced by Papadimitriou and Vempala.