Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Computation of minimal length full Steiner trees on the vertices of a convex polygon

Author: E. J. Cockayne
Journal: Math. Comp. 23 (1969), 521-531
MSC: Primary 05.45; Secondary 65.00
MathSciNet review: 0249323
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A Steiner minimal tree is a tree of minimal length whose vertices are a given set of points $ {a_1}, \cdots ,{a_n}$ in $ {E^2}$ and any set of additional points $ {s_1}, \cdots ,{s_k}(k \geqq 0)$. In general, the introduction of extra points makes possible shorter trees than the minimal length tree whose vertices are precisely $ {a_1}, \cdots ,{a_n}$ and for which practical algorithms are known. A Steiner minimal tree is the union of special subtrees, known as full Steiner trees. This paper demonstrates the use of the computer in generating minimal length full Steiner trees on sets of points in $ {E_2}$ which are the vertices of convex polygons. The procedure given is a basis from which further research might proceed towards an ultimate practical algorithm for the construction of Steiner minimal trees.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 05.45, 65.00

Retrieve articles in all journals with MSC: 05.45, 65.00

Additional Information

Article copyright: © Copyright 1969 American Mathematical Society

American Mathematical Society