Return to search
## On the steiner problem

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

Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/41202 |

Date | January 1967 |

Creators | Cockayne, Ernest |

Publisher | University of British Columbia |

Source Sets | University of British Columbia |

Language | English |

Detected Language | English |

Type | Text, Thesis/Dissertation |

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. |

Page generated in 0.002 seconds