Improved Approximation Algorithm for the (1,2)-Partial-Terminal Steiner Tree Problem

Given a complete graph G = (V,E) with a metric cost function c : E → R and two vertex subsets R ⊂ V and R ⊆ R, a partial-terminal Steiner tree is a Steiner tree which contains all the vertices in R such that all the vertices in R are leaves. The partial-terminal Steiner tree problem (PTSTP) is to find a partial-terminal Steiner tree with the minimum cost. The problem has been shown to be NP-hard and MAX SNPhard, even when the edge costs are restricted in {1, 2}, namely, the (1,2)-partial-terminal Steiner tree problem (PTSTP(1,2)). In this paper, we consider PTSTP(1,2). The previous best-known approximation ratio of PTSTP(1,2) was at most 1.79. In this paper, we propose a polynomialtime approximation algorithm that improves the approximation ratio from 1.79 to 1.67.