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Optimising declines in underground mines
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 theExpand
Probability Steiner trees and maximum parsimony in phylogenetic analysis
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 developedExpand
Determining the open pit to underground transition: A new method
TLDR
In this paper we provide a review of existing approaches to the transition problem encompassing: graph-theory based optimisation employing an opportunity cost approach; heuristics and integer programming. Expand
Optimum Steiner ratio for gradient-constrained networks connecting three points in 3-space, part I
TLDR
We show that in the gradient-constrained cases, the configuration of three terminals giving the minimum Steiner ratio is also an equilateral triangle. Expand
Designing Optimal Flow Networks
TLDR
We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. Expand
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 theExpand
Full Minimal Steiner Trees on Lattice Sets 1 M . Brazil
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. TheExpand
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 evolutionaryExpand
Optimal location of an underground connector using discounted Steiner tree theory
TLDR
The objective of this paper is to demonstrate that the gradient-constrained discounted Steiner point algorithm (GCDSPA) described in an earlier paper by the authors is applicable to a class of real mine planning problems by using the algorithm to design a part of the underground access in the Rubicon gold mine near Kalgoorlie in Western Australia. Expand
Computing Steiner points for gradient-constrained minimum networks
TLDR
We develop an algorithm for computing locally minimal Steiner points based on information from the labellings of adjacent edges. Expand
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