| Summary: | 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. === Science, Faculty of === Mathematics, Department of === Graduate
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