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On the steiner problem Cockayne, Ernest
Abstract
The classical Steiner Problem may be stated: Given n points [formula omitted] in the Euclidean plane, to construct the shortest tree(s) (i.e. undirected, connected, circuit free graph(s)) whose vertices include [formula omitted]. The problem is generalised by considering sets in a metric space rather than points in E² and also by minimising a more general graph function than length, thus yielding a large class of network minimisation problems which have a wide variety of practical applications, The thesis is concerned with the following aspects of these problems. 1. Existence and uniqueness or multiplicity of solutions. 2. The structure of solutions and demonstration that minimising trees of various problems share common properties. 3. Solvability of problems by Euclidean constructions or by other geometrical methods.
Item Metadata
Title |
On the steiner problem
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1967
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Description |
The classical Steiner Problem may be stated: Given n points
[formula omitted] in the Euclidean plane, to construct the shortest tree(s)
(i.e. undirected, connected, circuit free graph(s)) whose vertices
include [formula omitted].
The problem is generalised by considering sets in a metric
space rather than points in E² and also by minimising a more general
graph function than length, thus yielding a large class of network
minimisation problems which have a wide variety of practical applications,
The thesis is concerned with the following aspects of these
problems.
1. Existence and uniqueness or multiplicity of solutions.
2. The structure of solutions and demonstration that
minimising trees of various problems share common
properties.
3. Solvability of problems by Euclidean constructions or by
other geometrical methods.
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Genre | |
Type | |
Language |
eng
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Date Available |
2012-03-07
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0080622
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
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Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.