An Improved Approximation Algorithm for the Terminal Steiner Tree Problem

Abstract

Given a complete graph G = (V,E) with a length function on edges and a subset R of V, the terminal Steiner tree is defined to be a Steiner tree in G with all the vertices of R as its leaves. Then the terminal Steiner tree problem is to find a terminal Steiner tree in G with minimum length. In this paper, we present an approximation algorithm with performance ratio \(2\rho-\frac{(\rho\alpha^2-\alpha\rho)}{(\alpha+\alpha^2)(\rho-1)+2(\alpha-1)^2}\) for the terminal Steiner tree problem, where ρ is the best-known performance ratio for the Steiner tree problem with any α ≥ 2. When we let α = 3.87 ≈ 4, this result improves the previous performance ratio of 2.515 to 2.458.