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Optimising declines in underground mines

- M. Brazil, D. H. Lee, M. Van Leuven, J. Rubinstein, D. Thomas, N. Wormald
- Engineering
- 1 December 2003

Abstract This paper describes a method for optimising the layout of a decline in an underground mine. It models a decline as a mathematical network connecting the access points at each level of the… Expand

Probability Steiner trees and maximum parsimony in phylogenetic analysis

- J. Weng, I. Mareels, D. Thomas
- Mathematics, Medicine
- Journal of mathematical biology
- 1 June 2012

The phylogenetic tree (PT) problem has been studied by a number of researchers as an application of the Steiner tree problem, a well-known network optimisation problem. Of all the methods developed… Expand

Determining the open pit to underground transition: A new method

- D. Whittle, M. Brazil, P. A. Grossman, J. Rubinstein, D. Thomas
- Computer Science, Mathematics
- 17 September 2015

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Optimum Steiner ratio for gradient-constrained networks connecting three points in 3-space, part I

- K. Prendergast, D. Thomas, J. Weng
- Computer Science
- Networks
- 2009

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Designing Optimal Flow Networks

- M. Volz, M. Brazil, K. Swanepoel, D. Thomas
- Computer Science, Mathematics
- WCE
- 1 March 2009

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1 1 Ju l 2 01 3 Approximating Minimum Steiner Point Trees in Minkowski Planes ∗ M . Brazil

Given a set of points, we define a minimum Steiner point tree to be a tree interconnecting these points and possibly some additional points such that the length of every edge is at most 1 and the… Expand

Full Minimal Steiner Trees on Lattice Sets 1 M . Brazil

- J. Rubinstein, D. Thomas, J. Weng, N. Wormald
- 1997

Given a finite set of points P in the Euclidean plane, the Steiner problem asks us to constuct a shortest possible network interconnecting P. Such a network is known as a minimal Steiner tree. The… Expand

A Steiner Tree , Substitution Matrix Method for Reconstructing Phylogenetic Trees

Evolutionary theory implies that existing or extinct organisms are descended from a common ancestor. Hence, given a set of organisms, a phylogenetic tree can be reconstructed showing the evolutionary… Expand

Optimal location of an underground connector using discounted Steiner tree theory

- K. G. Sirinanda, M. Brazil, P. A. Grossman, J. Rubinstein, D. Thomas
- Computer Science
- 1 July 2020

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Computing Steiner points for gradient-constrained minimum networks

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