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Recently submitted papers
- M. Volz, M. Brazil, D.A. Thomas,
'The Gradient-Constrained Fermat-Weber Problem',
Geometriae Dedicata, submitted (2008).
- X. Wang, B. Moran, M. Brazil,
'Hyperbolic Positioning Using RIPS Measurements for Wireless Sensor Networks',
15th IEEE International Conference on Networks (ICON2007),
submitted (2007)
Refereed Journal Papers and Book Chapters
- M. Brazil, C.J. Ras, D.A. Thomas,
'Approximating Minimum Steiner Point Trees in Minkowski Planes',
Networks,
in press (accepted November 2009)
- J. Egeblad, B. K. Nielsen, M. Brazil,
'Translational packing of arbitrary polytopes',
Computational Geometry: Theory and Applications,
42 (May 2009), 269 - 288.
- M. Brazil, M. Zachariasen,
'Steiner Trees for Fixed Orientation Metrics',
J. Global Optimization,
43 (2009), 141 - 169.
Abstract
- M. Brazil, B. K. Nielsen, D.A. Thomas, P. Winter, M. Zachariasen,
'A Novel Approach to Phylogenetic Trees: d-Dimensional Geometric Steiner Trees',
Networks, 53 (2009), 104 - 111.
Abstract
- M. Brazil, P.A. Grossmann, D.H. Lee, J.H. Rubinstein, D.A. Thomas, N.C. Wormald,
'Decline design in underground mines using
constrained path optimisation',
Mining Technology: Trans. of the Institution of Mining and Metallurgy, Section A,
117 (2008), 93 - 99.
- M. Brazil, J.M. Smith, D.A. Thomas, J.F. Weng,
'Equivalence, Indicators, Quasi-indicators and Optimal Steiner
Topologies on Four Points in Space',
Fundamenta Informaticae,
84 (2008), 135 - 149.
Abstract
- M. Brazil, D.A. Thomas, J.F. Weng,
'Gradient-Constrained Minimum Networks. II. Labelled or Locally Minimal Steiner Points ',
J. Global Optimization, 42 (2008), 23 - 37.
Abstract
- C. Alford, M. Brazil, D.H. Lee,
'Optimisation in Underground Mining',
in Handbook on Operations Research in Natural
Resources,
New York: Springer
2007, 561 - 577.
Abstract
- D. Thomas, M. Brazil, D.H. Lee, N.C. Wormald,
'Network modelling of underground mine layout:
two case studies',
International Transactions in Operational Research,
14 (2007), 143 - 158.
Abstract
- M. Brazil, D. Thomas,
'Network Optimisation for the Design of Underground Mines',
Networks,
49 (2007), 40 - 50 .
Abstract
- M. Brazil, D.A. Thomas, J.F. Weng,
'Locally Minimal Uniformly Oriented Steiner Trees ',
Discrete Applied Mathematics,
154 (2006), 2545 - 2564
Abstract
- M. Brazil, D.A. Thomas, J.F. Weng, M. Zachariasen,
'Canonical Forms and Algorithms for Steiner Trees in Uniform Orientation Metrics ',
Algorithmica,
44 (2006), 281 - 300 .
Abstract, PDF
- M. Brazil, D.H. Lee, J.H. Rubinstein, D.A. Thomas, J.F. Weng, N.C. Wormald,
'Optimisation in the design of underground mine access',
in Uncertainty and Risk Management in Orebody Modelling and Strategic Mine Planning: Spectrum Series Volume 14,
Melbourne, Australia: Australasian Institute of Mining and Metallurgy, 2005, 121 - 124.
Abstract, PDF
- M. Brazil, P. Winter, M. Zachariasen,
'Flexibility of Steiner Trees in
Uniform Orientation Metrics',
Networks,
46 (2005), 142 - 153.
Abstract
- M. Brazil, D.A. Thomas, J.F. Weng, D.H. Lee, J.H. Rubinstein,
'Cost Optimisation for Underground Mining Networks',
Optimization and Engineering,
6 (2005), 241 - 256.
Abstract, PDF
- M. Brazil, D.A. Thomas, J.F. Weng,
'Upper and Lower Bounds for the Lengths of Steiner Trees in 3-Space ',
Geometriae Dedicata,
109 (2004), 107-119.
Abstract
- M. Brazil, B. K. Nielsen, P. Winter, M. Zachariasen,
'Rotationally Optimal Spanning and Steiner Trees in
Uniform Orientation Metrics',
Computational Geometry: Theory and Applications,
29 (2004), 251-263.
Abstract, PDF
- M. Brazil, D.H. Lee, M. Van Leuven, J.H. Rubinstein, D.A. Thomas, N.C. Wormald,
'Optimising Declines in Underground Mines',
Mining Technology: Trans. of the Institution of Mining and Metallurgy, Section A,
112 (2003), 164-170.
Abstract
- C. Mangelsdorf, M. Brazil, A. Tordesillas,
'Getting Hooked on Mathematics Through Its Applications',
Teaching Mathematics and its applications,
22 (2003), 63-75.
Abstract
- M. Brazil, D.H. Lee, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N.C. Wormald,
'A Network Model to Optimise Cost in Underground Mine Design ',
Trans. South African Institute of Electrical Engineers,
93 (2002), 97-103.
Abstract
- M. Brazil, D.A. Thomas, J.F.
Weng,
'Forbidden Subpaths for Steiner Minimum Networks in Uniform
Orientation Metrics', Networks, 39 (2002), 186-202.
Abstract
- M. Brazil,
'Steiner minimum trees in uniform orientation metrics', in Steiner Trees in Industry,
Dordrecht/Boston/London: Kluwer Academic Publishers,
2001, 1-28.
Abstract
- M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N. Wormald,
'Gradient-Constrained Minimum Networks, I. Fundamentals',
J. Global Optimization, 21 (2001), 139 - 155.
Abstract
- M. Brazil, D.A. Thomas, J.F.
Weng,
'Minimum Networks in Uniform Orientation Metrics', SIAM J.
Comput., 30 (2000), 1579 - 1593.
Abstract
- M. Brazil, D.H. Lee, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N.C. Wormald,
'Network optimisation of underground mine design',
The Australasian Institute for Mining and Metallurgy Proc.,
305 (2000), 57-65
Abstract
- M. Brazil, D.A. Thomas, J.F.
Weng,
'On the Complexity of the Steiner Problem',
J. Combin. Optimization 4 (2000), 187-195.
Abstract
- M. Brazil, D.A. Thomas, J.F.
Weng,
'Rectilinear Steiner Minimal Trees on Parallel Lines', in Advances
in Steiner Trees, Dordrecht/Boston/London: Kluwer Academic Publishers,
2000, 29-37.
- M. Brazil, D.A. Thomas, J.F.
Weng,
'A Polynomial Time Algorithm for Rectilinear Steiner Trees with
Terminals Constrained to Curves', Networks 33 (1999), 145-155.
Abstract
- M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N.C. Wormald,
'Shortest Networks on Spheres', Network Design:
Connectivity and Facilites Location, (DIMACS series in discrete mathematics
and theoretical computer science) 40 (1998), 453-461.
Abstract
- M. Brazil, D.A. Thomas, J.F.
Weng,
'Gradient-Constrained Minimal Steiner Trees', Network Design:
Connectivity and Facilites Location, (DIMACS series in discrete mathematics
and theoretical computer science) 40 (1998), 23-38.
- M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N.C. Wormald,
'Minimal Steiner Trees for Rectangular Arrays of Lattice
Points', J.
Combin. Theory Ser. A 79 (1997), 181-208.
- M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N.C. Wormald,
'Full Minimal Steiner Trees on Lattice Sets', J.
Combin. Theory Ser. A 78 (1997), 51-91.
- M. Brazil, T. Cole, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N.C. Wormald,
'Minimal Steiner Trees for 2^k * 2^k
Square Lattices', J. Combin. Theory Ser. A 73 (1996),
91-110.
- M. Brazil,
'Calculating Growth Functions for Groups Using Automata', in W. Bosma
and A. van der Poorten (eds.), Computational Algebra and Number
Theory , Mathematics and Its Applications 325 ,
Dordrecht/Boston/London: Kluwer Academic Publishers, 1995.
- M. Brazil,
'Growth Functions for some Non-Automatic Baumslag-Solitar Groups',
Trans. Amer. Math. Soc. 342 (1994), 137-154.
- M. Brazil,
'Growth Functions for some One-Relator Monoids', Communications
in Algebra 21 (1993), 3135-3146.
- M. Brazil, J. Covington, C. Praeger, T. Pentilla and A. Woods,
'Maximal
Subgroups of Infintie Symmetric Groups', Proc. London Math. Soc.
68 (1992), 77-111.
- M. Brazil,
'Monoid Growth Functions for Braid Groups', International
Journal
of Algebra and Computation 1 (1991), 201-205.
Refereed Conference Papers
- M. Brazil, B. Moran, M. Morelande, D. Thomas,
'Distributed Self-Localisation in Sensor Networks using RIPS Measurements',
2007 International Conference of Wireless Networks (ICWN 2007),
London, UK, (July, 2007), 1476-1481. [Winner of Best Paper Award]
- M. Brazil, P.A. Grossman, D.H. Lee, J.H. Rubinstein, D. Thomas, N.C. Wormald,
'Constrained path optimisation for underground mine layout',
2007 International Conference of Applied and Engineering Mathematics (ICAEM 2007),
London, UK, (July, 2007), 856-861.
- M. Brazil, J.M. Smith, D.A. Thomas, J.F. Weng,
'Quasi-indicators and Optimal Steiner Topologies
on Four Points in Space',
Seventeenth Australasian Workshop on Combinatorial Algorithms (AWOCA 2006) , Uluru and King's Canyon, Australia, (July 2006) , (14 pages).
- M. Brazil, J.H. Rubinstein, M. Volz,
'The Gradient-Constrained Fermat-Weber Problem for Underground Mine Design',
Proceedings of the 18th National Conference
of the Australian Society for Operations Research , Perth, Australia, (Sep. 2005) , 16-23.
- M. Brazil, P. Winter, M. Zachariasen,
'Flexibility of Steiner Trees in Uniform Orientation Metrics',
15th International Symposium, ISAAC 2004,
LNCS 3341
Hong Kong, (Dec. 2004) , 196-208.
- M. Brazil, D. Thomas, J.F. Weng, P. Winter, M. Zachariasen,
'The Structure and Flexibility of Steiner Trees in Uniform Orientation Metrics',
Proceedings of 6th Int. Conference on Optimization: Techniques and Applications,
Ballarat, Australia, (Dec. 2004), (11 pages).
- M. Brazil, D.H. Lee, J.H. Rubinstein, D.A. Thomas, J.F. Weng, N.C. Wormald,
'Optimisation in the design of underground mine access
',
The International Symposium on "Orebody Modelling and Strategic Mine Planning:
Uncertainty and Risk Management",
Perth, Australia, (Nov. 2004), 3-6
Abstract
- M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F.
Weng,
'Modelling and Optimisation of a Weighted Network in an Underground Mine Design',
Proceedings of the 3rd International Conference
on control Theory and Applications , Pretoria, South Africa, (Dec. 2001) , 564-568.
- M. Brazil,
'Groups that Grow Rationally with Respect to any Finite Generating
Set', in Proceeding of the Sixth Annual Algebra Conference of
Victoria ,
Melbourne: Royal Melbourne Institute of Technology Technical
Report No. 1, 1989.
Papers in Preparation
- M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F.
Weng, N. Wormald,
'Gradient-Constrained Minimum Networks, II. Minimising
Perturbations', in preparation.
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