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Faster approximation algorithms for the rectilinear steiner tree problem

  • Ulrich Fößmeier
  • Michael Kaufmann
  • Alexander Zelikovsky
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 762)

Abstract

The classical Steiner Tree Problem requires a shortest tree spanning a given vertex subset within a graph G=(V, E). An important variant is the Steiner tree problem in rectilinear metric. Only recently two algorithms were found which achieve better approximations than the ’traditional’ one with a factor of 3/2. These algorithms with an approximation ratio of 11/8 are quite slow and run in time O(n3) and O(n5/2). A new simple implementation reduces the time to O(n3/2). As our main result we present efficient parameterized algorithms which reach a performance ratio of 11/8+ε for any ε>0 in time O(n · log2n), and a ratio of 11/8+log log n log n in time O(n · log3n).

Keywords

Algorithms Steiner tree Approximations 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Ulrich Fößmeier
    • 1
  • Michael Kaufmann
    • 1
  • Alexander Zelikovsky
    • 2
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversität TübingenTübingenGermany
  2. 2.Institute of MathematicsKishinevMoldova

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