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Compression Theorems and Steiner Ratios on Spheres
TLDR
Using the compression theorem, the Steiner ratio on spheres is proved to be the same as on the Euclidean plane, namely $$backslash \bar 3/2$$ . Expand
Steiner minimal trees for regular polygons
TLDR
It is shown that the set ofn equally spaced points yields the longest Steiner minimal tree among all sets ofn cocircular points on a given circle. Expand
The Shortest Network under a Given Topology
  • F. Hwang, J. Weng
  • Mathematics, Computer Science
  • J. Algorithms
  • 1 September 1992
TLDR
It is proved that if a Steiner tree (a tree such that no two edges meet at an angle less than 120°) exists with the given topology, then it is the shortest network. Expand
Minimum Networks in Uniform Orientation Metrics
TLDR
This paper uses the variational method to systematically study properties of minimum networks connecting any given set of points in a $\ lambda$-plane, in which all lines are in $\lambda$ uniform orientations, and proves a number of angle conditions for Steiner minimum $lambda$-trees. Expand
Degree-five Steiner points cannot reduce network costs for planar sets
TLDR
It is shown that a degree-five Steiner point can never appear in a least-cost planar network; that is, it is actedally increased in the cost of the network. Expand
Group Testing with Two and Three Defectives
TLDR
A population of n items consisting of d defectives and n d good ones is considered, where d is the maximum number of tests the group testing procedure requires to find the defectives in n items. Expand
Minimal Steiner Trees for 2k×2k Square Lattices
TLDR
This paper proves a conjecture that the minimal Steiner trees for the set of points comprising the vertices of a 2k×2ksquare lattice are given by Chung, Graham, and Gardner. Expand
Optimisation in the design of underground mine access
TLDR
The goals for the next phase of development for this project will be discussed, including speeding up the algorithms and allowing for heterogeneous materials, such as aquifers and faults, as additional costs rather than obstacles. Expand
Minimum Networks for Four Points in Space
The minimum network problem (Steiner tree problem) in space is much harder than the one in the Euclidean plane. The Steiner tree problem for four points in the plane has been well studied. InExpand
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