nonnegative costs ratio approximation edge 86-97 https://doi.org/10.1007/978-3-642-03367-4_8 MAX SNP minimum cost subgraph problem Given a connected graph G = (V,E) with nonnegative costs on edges, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$c:E\rightarrow {\mathcal R}^+$\end{document}, 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. approximation algorithm connected graph G R. chapters graph G 1.25-Approximation Algorithm for Steiner Tree Problem with Distances 1 and 2 Steiner tree problem 2022-09-02T16:11 cost SNPs long time true https://scigraph.springernature.com/explorer/license/ good approximation chapter node r time 2009 distance 1 subset algorithm 2009-01-01 subgraphs general problem tree problem Springer Nature Department of Computer Science, Georgia State University, 30303, Atlanta, GA, USA Department of Computer Science, Georgia State University, 30303, Atlanta, GA, USA pub.1026258834 dimensions_id Piotr Berman Karpinski Marek Sack Jörg-Rüdiger Information and Computing Sciences 978-3-642-03366-7 Algorithms and Data Structures 978-3-642-03367-4 Computation Theory and Mathematics 10.1007/978-3-642-03367-4_8 doi Alexander Zelikovsky Dehne Frank Department of Computer Science, University of Bonn, 53117, Bonn, Germany Department of Computer Science, University of Bonn, 53117, Bonn, Germany Springer Nature - SN SciGraph project Gavrilova Marina Department of Computer Science & Engineering, Pennsylvania State University, University Park, 16802, PA, USA Department of Computer Science & Engineering, Pennsylvania State University, University Park, 16802, PA, USA Csaba D. Tóth