1.25-Approximation Algorithm for Steiner Tree Problem with Distances 1 and 2

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Given a connected graph G = (V,E) with nonnegative costs on edges, \(c:E\rightarrow {\mathcal R}^+\) , and a subset of terminal nodes R ⊂ V, the Steiner tree problem asks for the minimum cost subgraph of G spanning R. The Steiner Tree Problem with distances 1 and 2 (i.e., when the cost of any edge is either 1 or 2) has been investigated for long time since it is MAX SNP-hard and admits better approximations than the general problem. We give a 1.25 approximation algorithm for the Steiner Tree Problem with distances 1 and 2, improving on the previously best known ratio of 1.279.