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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
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
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
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
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
We develop an algorithm for computing locally minimal Steiner points based on information from the labellings of adjacent edges. Expand