Steiner minimal tree for points on a circle-Reference-Cited by-同舟云学术

Steiner minimal tree for points on a circle

Published:1985 Issue:4 Volume:95 Page:613-618
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Du D. Z.,Hwang F. K.,Chao S. C.

Abstract

We show that the Steiner minimal tree for a set of points on a circle is the shortest path connecting them if at most one distance between two consecutive points is "large". We prove this by making an interesting use of the Steiner ratio ρ \rho which has been well studied in the literature.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1985-095-04/S0002-9939-1985-0810173-6/S0002-9939-1985-0810173-6.pdf

Reference7 articles.

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2. A new bound for the Steiner ratio;Du, D. Z.;Trans. Amer. Math. Soc.,1983

3. The complexity of computing Steiner minimal trees;Garey, M. R.;SIAM J. Appl. Math.,1977

4. Steiner minimal trees;Gilbert, E. N.;SIAM J. Appl. Math.,1968

5. R. L. Graham, Some results on Steiner minimal trees, unpublished manuscript.

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