Lower bounds for the relative greedy algorithm for approximating Steiner trees

  • Authors:

  • Stefan Hougardy;Stefan Kirchner

  • Affiliations:

  • Humboldt-Universität zu Berlin, Institut für Informatik, 10099 Berlin, Germany;Humboldt-Universität zu Berlin, Institut für Informatik, 10099 Berlin, Germany

  • Venue:
  • Networks
  • Year:
  • 2006

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Abstract

The Steiner tree problem is to find a shortest subgraph that spans a given set of vertices in a graph. This problem is known to be NP-hard, and it is well known that a polynomial time 2-approximation algorithm exists. In 1996, Zelikovsky suggested an approximation algorithm for the Steiner tree problem that is called the relative greedy algorithm. Until now the performance ratio of this algorithm has not been known. Zelikovsky provided 1.694 as an upper bound, and Gröpl, Hougardy, Nierhoff, and Prömel proved that 1.333 is a lower bound. In this article we improve the lower bound for the performance ratio of the relative greedy algorithm to 1.385. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(2), 111–115 2006