๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Steiner minimal trees on regular polygons with centre

โœ Scribed by J.F. Weng; R.S. Booth

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
594 KB
Volume
141
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Let P,,n~>3, be the set of vertices of a regular n-gon and o be the centre of P,. Let P+ = P, u [o}. In this paper we determine the Steiner minimal trees on P+. By this example we will see how complicated the Steiner problem may become if even one regular point not lying on the Steiner polygon is added.

๐Ÿ“œ SIMILAR VOLUMES

Full Minimal Steiner Trees on Lattice Se
Full Minimal Steiner Trees on Lattice Sets
โœ M. Brazil; J.H. Rubinstein; D.A. Thomas; J.F. Weng; N.C. Wormald ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 497 KB

Given a finite set of points P in the Euclidean plane, the Steiner problem asks us to constuct a shortest possible network interconnecting P. Such a network is known as a minimal Steiner tree. The Steiner problem is an intrinsically difficult one, having been shown to be NP-hard [7]; however, it oft

Variational approach and Steiner minimal
Variational approach and Steiner minimal trees on four points
โœ J.F. Weng ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 691 KB

A Steiner topology t, is defined to be a degenerate topology of another Steiner topology t, if t, is obtained from t, by sequentially collapsing Steiner points into their adjacent regular points of degree less than three. A full topology t is called optimal if there is a Steiner minimal tree whose t