Chapter

Algorithms and Data Structures

Volume 5664 of the series Lecture Notes in Computer Science pp 86-97

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

  • Piotr BermanAffiliated withDepartment of Computer Science & Engineering, Pennsylvania State University
  • , Marek KarpinskiAffiliated withDepartment of Computer Science, University of Bonn
  • , Alexander ZelikovskyAffiliated withDepartment of Computer Science, Georgia State University

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.