Annals of Operations Research

, Volume 33, Issue 7, pp 549–556 | Cite as

A simple proof of Hwang's theorem for rectilinear Steiner minimal trees

  • D. S. Richards
  • J. S. Salowe
Section VII Computational Geometry And TND

Abstract

We present a simple, direct proof of Hwang's characterization of rectilinear Steiner minimal trees [3]: LetS be a set of at least five terminals in the plane. If no rectilinear Steiner minimal tree forS has a terminal of degree two or more, there is a tree in which at most one of the Steiner points does not lie on a straight linel, and the tree edges incident to the Steiner points onl appear on alternate sides. This theorem has been found useful in proving other results for rectilinear Steiner minimal trees.

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References

  1. [1]
    P.K. Agarwal and M.I. Shing, Algorithms for the special cases of rectilinear Steiner trees: I. Points on the boundary of a rectilinear rectangle, Networks 20(1990)453–485.Google Scholar
  2. [2]
    J.P. Cohoon, D.S. Richards and J.S. Salowe, An optimal Steiner tree algorithm for a net whose terminals lie on the perimeter of a rectangle, IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems 9(1990)398–407.Google Scholar
  3. [3]
    F.K. Hwang, On Steiner minimal trees with rectilinear distance, SIAM J. Appl. Math. 30(1976)104–114.Google Scholar

Copyright information

© J.C. Baltzer AG, Scientific Publishing Company 1991

Authors and Affiliations

  • D. S. Richards
    • 1
  • J. S. Salowe
    • 1
  1. 1.Department of Computer ScienceUniversity of VirginiaCharlottesvilleUSA

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