Book
Chapters:
[9]
Polynomial Time Algorithm for the Rectilinear Steiner Tree problem, Steiner
Trees in Industry (Eds. X. Cheng and D-Z. Du), Kluwer Academic Publishers,
406-426, 2001. (with D.A.thomas)
[8] Minimum
Networks for Separating and Surrounding Objects, Steiner Trees in Industry
(Eds. X. Cheng and D-Z. Du), Kluwer Academic Publishers, 427-440, 2001.
[7]
Shortest Networks for One Line and Two Points in Space, Advances in Steiner
Trees (Eds. D-Z. Du, J.
M. Smith and J. H. Rubinstein), Kluwer Academic Publishers, 15-26, 2001. (with R.Booth and D.A.Thomas).
[6]
Rectilinear Steiner Minimal Trees on Parallel Lines, Advances in Steiner
Trees (Eds. D-Z. Du, J.
M. Smith and J. H. Rubinstein), Kluwer Academic Publishers, 27-38, 2001. (with M.Brazil and D.A.Thomas).
[5] Steiner
Trees, Coordinate Systems and NP-hardness, Advances in Steiner Trees
(Eds. D-Z. Du, J. M. Smith
and J. H. Rubinstein), Kluwer
Academic Publishers, 63-80,
2000.
[4] Minimum
Networks on Surfaces, Handbook of Combinatorial Optimization, Vol. 2
(Eds. D-Z. Du and P. M. Pardalos), Kluwer Academic Publishers, 1998, 589-516.
[3]
Gradient-constrained minimal Steiner trees, DIMACS Series, Vol. 40 (Eds.
P. M. Pardalos and D-Z. DU), American Mathematical Society, 1998, 453-461.
(with M.Brazil, and D.A.Thpma)
[2] A New
Model of Generalized Steiner Trees and 3-Coordinate Systems, DIMACS Series,
Vol. 40 (Eds. P. M. Pardalos and D-Z. DU), American Mathematical Society, 1998,
415-424.
[1]
Shortest networks on spheres, DIMACS Series, Vol. 40 (Eds. P. M.
Pardalos and D-Z. DU), American Mathematical Society, 1998, 453-461. (with
M.Brazil, J.H.Rubinatein, D.A.Thpma and N.C.Wormald).
Journal
Papers:
[52]
Equivalence, indicators, Quasi-indicators and Optimal Steiner Topologies on
Four Points in Space (Invited
paper), 84(1), 135-149, 2008, Fundamenta Informaticae, (with J. MacGregor Smith, M. Brazil and D.A.
Thomas).
[51] Gradient-Constrained Minimum Networks. II: Labelled or Locally Minimal Steiner Points, J. Global Optimization, (with M. Brazil and D.A. Thomas).
[50] Gradient-Constrained Minimum Networks: An Algorithm for Computing Steiner, Discrete Optimization, accepted (with D.A. Thomas).
[49] Locally
Minimal Uniformly Oriented Shortest Networks, Discrete Applied
Mathematics, accepted (with M.
Brazil and D.A. Thomas).
[48] Minimum
Cost Flow-Dependent Communication Networks, Networks, Vol. 48, 39-46, 2006 (with D.A. Thomas).
[47] Approximations and lower bounds for the length of minimal Euclidean Steiner trees , J. Global Optimization, Vol. 35, 573-592, 2006, (with J.H.Rubinstein and N.Wormald).
[46] Cost Optimisation for Underground Mining Networks,
Optimisation and Engineering, Vol. 6, 2005, 241-256 (with M. Brazil, J.
H. Rubinstein, D. A. Thomas and D. H. Lee).
[45]
Canonical Forms and Algorithms for Steiner Trees in Uniform Orientation
Metrics, Algotirhmica (Online), DOI: 10.1007/s00453-005-1178-6,
30 September, 2005, (with M. Brazil, D.A. Thomas and M. Zachariasen).
[44] Optimisation in the Design of Underground Mine Access in Uncertainty and Risk Management in Orebody Modelling and Strategic Mine Planning (Edited by Roussos Dimitrakopoulos), AusIMM Spectrum Series, Vol 14, 121 – 124, 2005 (with M. Brazil, D. Lee, J.H. Rubinstein, D.A. Thomas and N.C. Wormald).
[43]
Exactly Solvable and Unsolvable Shortest Network Problems in 3D-space, Contributions
to Algebra and Geometry, Vol. 45, 649-663, 2004 (with R.S. Booth and D.A.
Thomas).
[42] Upper
and Lower Bounds for the Lengths of Steiner Trees in 3-Space, Geometriae
Dedicata, Vol. 109, 107-119, 2004 (with M. Brazil and D.A. Thomas).
[41] A
Network Model to Optimise Cost in Underground Mine Design, Transactions of
the South African Institute of Electrical Engineers, Vol. 93, 97-103, 2002 (with M.
[40]
Generalized Melzak's Construction in the Steiner Tree Problem, International
Journal of Computational Geometry and Applications, Vol. 12, 481-488, 2002.
[39]
Minimum Networks for Four Point in Space, Geometriae Dedicata, Vol.
93, 57-70, 2002 (with J.H. Rubinstein
and D.A. Thomas).
[38]
Forbidden Subpaths for Steiner Minimum Networks in Uniform Orientation Metrics,
Networks, Vol. 39, 186-202, 2002 (with M. Brazil and D.A. Thomas).
[37]
Gradient-Constrained Minimum Networks, I. Fundamentals, J. Global
Optimization, Vol. 21, 139-155, 2001
(with M. Brazil, J.H. Rubinstein, D.A. Thomas and N.C. Wormald).
[36] Steiner
Minimal Trees with One Polygonal Obstacle, Algorithmica, Vol. 29,
638-648, 2001, (with J.M. Smith).
[35]
Steiner Trees on Curved Surfaces, Graphs and Combinatorics, Vol. 17,
353-363, 2001.
[34]
Network Optimization of Underground Mine Design, The AusIMM Proceedings, Vol. 305, No. 1, 57-65, 2000 (with M.
Brazil, D.H. Lee, J.H. Rubinstein, D.A. Thomas and N.C. Wormald).
[33] On the Complexity of the
Steiner Problem, J. Combin. Optimization, Vol. 4, 187-195, 2000 (with M.
Brazil and D.A. Thomas).
[32] Minimum
Networks in Uniform Orientation Metrics, SIAM J. Comput., Vol. 30, 2000,
1579-1593 (with M. Brazil, D.A. Thomas).
[31] A Note
on the Compression Theorem for Convex Surfaces, Discrete Math., Vol 212,
2000, 257-260, (with J.H. Rubinstein).
[30] Pseudo-Gilbert-Steiner
Trees, Networks, Vol. 33, 1999, 175-178 (with D. Trietsch).
[29] A
Polynomial Time Algorithm for Rectilinear Steiner Trees with Terminals
Constrained to Curves, Networks, Vol. 33, 1999, 145-155 (with M. Brazil
and D.A. Thomas).
[28] Minimal
Steiner Trees for Rectangular Arrays of Lattice Points, J. Combin. Theory,
Vol. 79, 1997, 181-208, (with M. Brazil, J.H. Rubinstein, D.A. Thomas and N.C.
Wormald).
[27] Full
Minimal Steiner Trees on Lattice Sets, J. Combin. Theorey, Vol.79, 1997,
51-91, (with M. Brazil, J.H. Rubinstein, D.A. Thomas and N.C. Wormald).
[26] Linear
Steiner Trees for Infinite Spirals,
[25]
Shortest Networks for Smooth Curves,
[24]
Expansion of Linear Steiner Trees, Algorithmica, Vol. 19, 1997, 318-330.
[23]
Compression Theorem and Steiner Ratios on Spheres, J. Combin. Optimization,
Vol. 1, 1997, 67-78, (with J.H. Rubinstein)
[22]
Steiner Minimal Trees on the
[21]
Minimal Steiner Trees for 2k´ 2k Square Lattices, J.
Combin. Theory, Vol. 73, 1996, 91-110, (with M. Brazil, T. Cole, J.H.
Rubinstein, D.A. Thomas and N.C.
Wormald).
[20]
Steiner Minimal Trees on Regular Polygons with Center, Discrete. Math.,
Vol. 141, 1995, 259-274 (with R.S. Booth).
[19]
Steiner Polygons in the Steiner Problem, Geometriae Dedicata, Vol. 52,
1994, 119-127.
[18]
Determining Shortest Networks in the Euclidean Plane, Bull. Australian Math.
Soc., Vol. 48, 1994, 349-350.
[17]
Variational Approach and Steiner Minimal Trees on Four Points, Discrete.
Math., Vol. 132, 1994, 349-362.
[16]
Symmetrization Theorem of Full Steiner Topologies, J.Combin. Theory,
Vol. 66, 1994, 185-191.
[15] An
Optimal Group Testing Algorithm on k-Disjoint Sets, Oper. Res.
Letters, Vol. 13, 1993, 43-44 (with F.K. Hwang).
[14]
Degenerate Gilbert-Steiner Trees, Networks, Vol.22, 1992, 335-348.
[13] Degree
Five Steiner Points Cannot Reduce Network Costs for Planar Sets, Networks,
Vol. 22, 1992, 531-537 (with J.H. Rubinstein and D.A. Thomas).
[12] the
Shortest Network Under a Given Topology, J. of Algorithm, Vol. 13, 1992,
468-488, (with F.K. Hwang).
[11] Steiner
Minimal Trees for a Class of Zigzag Lines, Algorithmica, Vol. 7, 1992,
231-246 (with R.S. Booth).
[10] Group
Testing with Two and Three Defectives,
[9] Optimal
Detection of Two Defectives with a Parity Check
[8] Steiner
Minimal Trees for Regular Polygons, Discrete Comput. Geometry, Vol.2,
1987, 65-84, (with D.Z. Du and F.K. Hwang).
[7] Partial
Elementary Equivalence of Groups (1) (in Chinese), J. of Beijing Normal
Univ., No.3, 1986, 7-12, (with S.Q. Wang).
[6]
Hexagonal Coordinate System and Steiner Minimal Trees, Discrete. Math.,
Vol.62, 1986, 49-57, (with F.K. Hwang).
[5]
Generalized Steiner Problem and Hexagonal Coordinate System (in Chinese), Acta
Math. Appl. Sinica, Vol.8, 1985, 383-397.
[4] Steiner
Minimal Trees on Vertices of Regular Polygons (in Chinese), Acta Math. Appl.
Sinica, Vol.8, 1985, 129-141.
[3] A Class
of Full Steiner Minimal Trees, Discrete. Math., Vol.45, 1983, 107-112,
(with D.Z. Du and F.K. Hwang).
[2] Steiner
Minimal Trees on Zig-Zag Lines, Trans. Amer. Math. Soc., Vol.278, 1983, 149-156, (with D.Z.
Du and F.K. Hwang).
[1]
Conference
Papers:
[7]
Quasi-indicators and optimal Steiner topologies on four points in space, Proceedingsof
AWOCA2006, 54-66, 2006 (with J.Macgregor, Smith, M. Brazil
and D.A. Thomas).
[6] A Note on Distance-Based Geographic Location in Sensor Networks, Proceedings of International Symposium on Communications and Information Technologies (ISCIT2005, Beijing, October 2005), IEEE Catalog Number: 05EX1224, pp. 681-684 (with D.A. Thomas).
[5] The structure and flexibility of
Steiner trees in uniform orientation metrics, 6th ICOTA, December 2004, Ballarat
[4] An Algorithm for
Computing Steiner Points in Gradient-Constrained Minimum Networks, 3th ICCM, December 2004, Hongkong (with D.A. Thomas).
[3] Constructing minimum cost flow-dependent networks, Network Design and Management, Proceedings of SPIE, Vol. 4909, 2002, 239-247 (with D.A. Thomas).
[2], Modelling and optimisation of a weighted networks in an underground mine design, Proceedings of the 3rd International Conference on Control Theory and Applications, 564-568, 2001 (with M. Brazil, J.H. Rubinstein and D.A. Thomas).
[1] Network optimization of underground mine design, The AusIMM Proceedings, Vol. 305, 1-9, 2000 (with M. Brazil, D.H. Lee, J.H. Rubinstein, D.A. Thomas and N.C. Mormald).