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

  • Authors:

  • Piotr Berman;Marek Karpinski;Alexander Zelikovsky

  • Affiliations:

  • Department of Computer Science & Engineering, Pennsylvania State University, 16802;Department of Computer Science, University of Bonn, Bonn, 53117;Department of Computer Science, Georgia State University, Atlanta, 30303

  • Venue:
  • WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
  • Year:
  • 2009

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Abstract

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.