On the Approximability of the Steiner Tree Problem

We show that it is not possible to approximate the minimum Steiner tree problem within 1 + 1 162 unless RP = NP. The currently best known lower bound is 1 + 1 400. The reduction is from H˚astad’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. Key words: Minimum Steiner tree, Approximability, Gadget reduction, Lower bounds.

• Type: Conference
• Year: 2001
• Where: MFCS
• Authors: Martin Thimm
• Keywords: Lower Bounds, MFCS 2001, Minimum Steiner Tree, Steiner Tree Problem, Theoretical Computer Science