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A fast algorithm for Steiner trees


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.

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Kou, L., Markowsky, G. & Berman, L. A fast algorithm for Steiner trees. Acta Informatica 15, 141–145 (1981).

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  • Computational Mathematic
  • System Organization
  • Time Complexity
  • Distance Function
  • Optimal Tree