Minimal steiner trees on square lattices
The paper gives a general approach in constructing minimal trees using Steiner points. Steiner points are the points added in a given set of points, used to minimize the length of the network connecting the original set of points. Such a network is called a Steiner tree. A square lattice is a set of...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
| Published: |
Animo Repository
1992
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| Subjects: | |
| Online Access: | https://animorepository.dlsu.edu.ph/etd_bachelors/16028 |
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| Institution: | De La Salle University |
| Language: | English |
| Summary: | The paper gives a general approach in constructing minimal trees using Steiner points. Steiner points are the points added in a given set of points, used to minimize the length of the network connecting the original set of points. Such a network is called a Steiner tree. A square lattice is a set of points arranged in the form of a square. The conjectured minimal Steiner trees for square lattice of orders 2 to 14 are presented here. To construct minimal Steiner trees for square lattices of orders bigger than 14, a core square with a folded band of width 3 is used.The formulas, illustrations and theorems discussed in the thesis came from the articles, Steiner Trees on a Checkerboard by Fan Chung, Martin Gardner and Ron Graham, and Steiner minimal Trees by E. N. Gilbert and H. O. Pollack. |
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