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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Steiner minimal trees on zig-zag lines

Authors: D. Z. Du, F. K. Hwang and J. F. Weng
Journal: Trans. Amer. Math. Soc. 278 (1983), 149-156
MSC: Primary 05C05; Secondary 51M15
MathSciNet review: 697066
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Abstract: A Steiner minimal tree for a given set $P$ of points in the Euclidean plane is a shortest network interconnecting $P$ whose vertex set may include some additional points. The construction of Steiner minimal trees has been proved to be an $NP$-complete problem for general $P$. However, the $NP$-completeness does not exclude the possibility that Steiner trees for sets of points with special structures can be efficiently determined. In this paper we determine the Steiner mimmal trees for zig-zag lines with certain regularity properties. We also give an explicit formula for the length of such a tree.

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Article copyright: © Copyright 1983 American Mathematical Society