Acta Informatica

, Volume 15, Issue 2, pp 141–145 | Cite as

A fast algorithm for Steiner trees

  • L. Kou
  • G. Markowsky
  • L. Berman


Given an undirected distance graph G=(V, E, d) and a set S, where V is the set of vertices in G, E is the set of edges in G, d is a distance function which maps E into the set of nonnegative numbers and S⊑V is a subset of the vertices of V, the Steiner tree problem is to find a tree of G that spans S with minimal total distance on its edges. In this paper, we analyze a heuristic algorithm for the Steiner tree problem. The heuristic algorithm has a worst case time complexity of O(¦S¦¦V¦2) on a random access computer and it guarantees to output a tree that spans S with total distance on its edges no more than 2(1−1/l) times that of the optimal tree, where l is the number of leaves in the optimal tree.


Computational Mathematic System Organization Time Complexity Distance Function Optimal Tree 
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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • L. Kou
    • 1
  • G. Markowsky
    • 1
  • L. Berman
    • 1
  1. 1.IBM Thomas J. Watson Research CenterYorktown HeightsUSA

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