Marcus'
Home Page

EEEng
Home Page

Recently submitted papers

1. M. Volz, M. Brazil, D.A. Thomas,
   'The Gradient-Constrained Fermat-Weber Problem',
   Geometriae Dedicata,
   submitted (2008).

2. 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

1. M. Brazil, C.J. Ras, D.A. Thomas,
   'Approximating Minimum Steiner Point Trees in Minkowski Planes',
   Networks, in press (accepted November 2009)
   

2. J. Egeblad, B. K. Nielsen, M. Brazil,
   'Translational packing of arbitrary polytopes',
   Computational Geometry: Theory and Applications,
   42 (May 2009), 269 - 288.
   

3. M. Brazil, M. Zachariasen,
   'Steiner Trees for Fixed Orientation Metrics',
   J. Global Optimization, 43 (2009), 141 - 169.
   Abstract

4. 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

5. 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.
   

6. 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

7. 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

8. 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

9. 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

10. M. Brazil, D. Thomas,
    'Network Optimisation for the Design of Underground Mines',
    Networks, 49 (2007), 40 - 50 .
    Abstract

11. M. Brazil, D.A. Thomas, J.F. Weng,
    'Locally Minimal Uniformly Oriented Steiner Trees ',
    Discrete Applied Mathematics, 154 (2006), 2545 - 2564
    Abstract

12. 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

13. 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

14. M. Brazil, P. Winter, M. Zachariasen,
    'Flexibility of Steiner Trees in Uniform Orientation Metrics',
    Networks, 46 (2005), 142 - 153.
    Abstract

15. 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

16. 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

17. 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

18. 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

19. C. Mangelsdorf, M. Brazil, A. Tordesillas,
    'Getting Hooked on Mathematics Through Its Applications',
    Teaching Mathematics and its applications,
    22 (2003), 63-75.
    Abstract

20. 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

21. M. Brazil, D.A. Thomas, J.F. Weng,
    'Forbidden Subpaths for Steiner Minimum Networks in Uniform
    Orientation Metrics',
    Networks, 39 (2002), 186-202.
    Abstract

22. M. Brazil,
    'Steiner minimum trees in uniform orientation metrics',
    in Steiner Trees in Industry,
    Dordrecht/Boston/London: Kluwer Academic Publishers, 2001, 1-28.
    Abstract

23. 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

24. M. Brazil, D.A. Thomas, J.F. Weng,
    'Minimum Networks in Uniform Orientation Metrics',
    SIAM J. Comput., 30 (2000), 1579 - 1593.
    Abstract

25. 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

26. M. Brazil, D.A. Thomas, J.F. Weng,
    'On the Complexity of the Steiner Problem',
    J. Combin. Optimization 4 (2000), 187-195.
    Abstract

27. 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.

28. 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

29. 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

30. 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.

31. 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.

32. 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.

33. 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.

34. 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.

35. M. Brazil,
    'Growth Functions for some Non-Automatic Baumslag-Solitar Groups',
    Trans. Amer. Math. Soc. 342 (1994), 137-154.

36. M. Brazil,
    'Growth Functions for some One-Relator Monoids',
    Communications in Algebra 21 (1993), 3135-3146.

37. 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.

38. M. Brazil,
    'Monoid Growth Functions for Braid Groups',
    International Journal of Algebra and Computation 1 (1991), 201-205.

Refereed Conference Papers

1. 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]

2. 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.

3. 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).

4. 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.

5. 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.

6. 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).

7. 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

8. 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.

9. 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

1. M. Brazil, J.H. Rubinstein, D.A. Thomas, J.F. Weng, N. Wormald,
   'Gradient-Constrained Minimum Networks, II. Minimising Perturbations',
   in preparation.