Finding a Noncrossing Steiner Forest in Plane Graphs Under a 2-Face Condition |
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Authors: | Yoshiyuki Kusakari Daisuke Masubuchi Takao Nishizeki |
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Institution: | (1) Department of Electronics and Information Systems, Akita Prefectural University, 84-4 Ebi-no-kuchi, Honjou-shi, Akita, 015-0055, Japan;(2) Thanks & Regards, IBM Japan Ltd., 19-21 Nihonbashi-Hakozaki-cho, Chuo-ku, Tokyo, 103-8510, Japan;(3) Graduate School of Information Sciences, Tohoku University, Aoba-yama 05, Sendai, 980-8579, Japan |
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Abstract: | Let G = (V,E) be a plane graph with nonnegative edge weights, and let
be a family of k vertex sets
, called nets. Then a noncrossing Steiner forest for
in G is a set
of k trees
in G such that each tree
connects all vertices, called terminals, in net N
i, any two trees in
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
if G has n vertices and each net contains a bounded number of terminals. |
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Keywords: | algorithm plane graph noncrossing Steiner tree |
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