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Finding a Noncrossing Steiner Forest in Plane Graphs Under a 2-Face Condition

Author

Listed:
  • Yoshiyuki Kusakari

    (Akita Prefectural University)

  • Daisuke Masubuchi

    (IBM Japan Ltd.)

  • Takao Nishizeki

    (Tohoku University)

Abstract

Let G = (V,E) be a plane graph with nonnegative edge weights, and let $$\mathcal{N}$$ be a family of k vertex sets $$N_1 ,N_2 ,...,N_k \subseteq V$$ , called nets. Then a noncrossing Steiner forest for $$\mathcal{N}$$ in G is a set $$\mathcal{T}$$ of k trees $$T_1 ,T_2 ,...,T_k$$ in G such that each tree $$T_i \in \mathcal{T}$$ connects all vertices, called terminals, in net N i, any two trees in $$\mathcal{T}$$ do not cross each other, and the sum of edge weights of all trees is minimum. In this paper we give an algorithm to find a noncrossing Steiner forest in a plane graph G for the case where all terminals in nets lie on any two of the face boundaries of G. The algorithm takes time $$O\left( {n\log n} \right)$$ if G has n vertices and each net contains a bounded number of terminals.

Suggested Citation

  • Yoshiyuki Kusakari & Daisuke Masubuchi & Takao Nishizeki, 2001. "Finding a Noncrossing Steiner Forest in Plane Graphs Under a 2-Face Condition," Journal of Combinatorial Optimization, Springer, vol. 5(2), pages 249-266, June.
    • Handle: RePEc:spr:jcomop:v:5:y:2001:i:2:d:10.1023_a:1011425821069
    DOI: 10.1023/A:1011425821069
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    References listed on IDEAS

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    1. Ranel E. Erickson & Clyde L. Monma & Arthur F. Veinott, 1987. "Send-and-Split Method for Minimum-Concave-Cost Network Flows," Mathematics of Operations Research, INFORMS, vol. 12(4), pages 634-664, November.
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