Forbidden subpaths for Steiner minimum networks in uniform orientation metrics

M. Brazil; D. A. Thomas; J. F. Weng

doi:10.1002/net.10025

Forbidden subpaths for Steiner minimum networks in uniform orientation metrics

Networks ◽

10.1002/net.10025 ◽

2002 ◽

Vol 39 (4) ◽

pp. 186-202 ◽

Cited By ~ 4

Author(s):

M. Brazil ◽

D. A. Thomas ◽

J. F. Weng

Keyword(s):

Minimum Networks

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GENERALIZED MELZAK'S CONSTRUCTION IN THE STEINER TREE PROBLEM

International Journal of Computational Geometry & Applications ◽

10.1142/s0218195902000992 ◽

2002 ◽

Vol 12 (06) ◽

pp. 481-488 ◽

Cited By ~ 2

Author(s):

JIA F. WENG

Keyword(s):

Steiner Tree ◽

Euclidean Plane ◽

Steiner Tree Problem ◽

Minimal Tree ◽

Steiner Minimal Tree ◽

The Core ◽

Steiner Minimal Trees ◽

Minimum Networks ◽

Set Of Points ◽

The Given

For a given set of points in the Euclidean plane, a minimum network (a Steiner minimal tree) can be constructed using a geometric method, called Melzak's construction. The core of the Melzak construction is to replace a pair of terminals adjacent to the same Steiner point with a new terminal. In this paper we prove that the Melzak construction can be generalized to constructing Steiner minimal trees for circles so that either the given points (terminals) are constrained on the circles or the terminal edges are tangent to the circles. Then we show that the generalized Melzak construction can be used to find minimum networks separating and surrounding circular objects or to find minimum networks connecting convex and smoothly bounded objects and avoiding convex and smoothly bounded obstacles.

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