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Author ID: brazil.marcus-n Recent zbMATH articles by "Brazil, Marcus N."
Published as: Brazil, M.; Brazil, Marcus; Brazil, Marcus N.
Documents Indexed: 60 Publications since 1991, including 1 Book
Co-Authors: 34 Co-Authors with 56 Joint Publications
916 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

45 Publications have been cited 209 times in 130 Documents Cited by Year
On the history of the Euclidean Steiner tree problem. Zbl 1295.05002
Brazil, Marcus; Graham, Ronald L.; Thomas, Doreen A.; Zachariasen, Martin
19
2014
Gradient-constrained minimum networks. I: Fundamentals. Zbl 1068.90605
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
13
2001
Translational packing of arbitrary polytopes. Zbl 1178.90286
Egeblad, Jens; Nielsen, Benny K.; Brazil, Marcus
12
2009
Optimal interconnection trees in the plane. Theory, algorithms and applications. Zbl 1319.05044
Brazil, Marcus; Zachariasen, Martin
12
2015
Network optimization for the design of underground mines. Zbl 1131.90410
Brazil, M.; Thomas, D. A.
12
2007
Growth functions for some nonautomatic Baumslag-Solitar groups. Zbl 0804.20027
Brazil, Marcus
11
1994
Canonical forms and algorithms for Steiner trees in uniform orientation metrics. Zbl 1095.68074
Brazil, M.; Thomas, D. A.; Weng, J. F.; Zachariasen, M.
9
2006
Minimum networks in uniform orientation metrics. Zbl 0973.05022
Brazil, M.; Thomas, D. A.; Weng, J. F.
9
2000
Steiner trees for fixed orientation metrics. Zbl 1169.90467
Brazil, M.; Zachariasen, M.
7
2009
Gradient-constrained minimum networks. II: Labelled or locally minimal Steiner points. Zbl 1168.90626
Brazil, M.; Thomas, D. A.; Weng, J. F.
6
2008
A novel approach to phylogenetic trees: \(d\)-dimensional geometric Steiner trees. Zbl 1168.92035
Brazil, M.; Thomas, D. A.; Nielsen, B. K.; Winter, P.; Wulff-Nilsen, C.; Zachariasen, M.
6
2009
Monoid growth functions for braid groups. Zbl 0789.20036
Brazil, Marcus
6
1991
Maximal subgroups of infinite symmetric groups. Zbl 0795.20002
Brazil, Marcus; Covington, Jacinta; Penttila, Tim; Praeger, Cheryl E.; Woods, Alan R.
6
1994
Curvature-constrained directional-cost paths in the plane. Zbl 1259.49068
Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A.
6
2012
Minimal Steiner trees for rectangular arrays of lattice points. Zbl 0883.05038
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
5
1997
Optimisation in underground mining. Zbl 1189.90088
Alford, Christopher; Brazil, Marcus; Lee, David H.
5
2007
Maximizing the net present value of a Steiner tree. Zbl 1338.90434
Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A.
5
2015
Generalised \(k\)-Steiner tree problems in normed planes. Zbl 1307.68083
Brazil, Marcus; Ras, Charl J.; Swanepoel, Konrad J.; Thomas, Doreen A.
5
2015
Minimal Steiner trees for \(2^ k \times 2^ k\) square lattices. Zbl 0844.05036
Brazil, M.; Cole, T.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
4
1996
The bottleneck 2-connected \(k\)-Steiner network problem for \(k \leq 2\). Zbl 1243.05064
Brazil, M.; Ras, C. J.; Thomas, D. A.
4
2012
Locally minimal uniformly oriented shortest networks. Zbl 1275.90114
Brazil, Marcus; Thomas, Doreen A.; Weng, Jia Feng
4
2006
Upper and lower bounds for the lengths of Steiner trees in 3-space. Zbl 1068.05014
Brazil, M.; Thomas, D. A.; Weng, J. F.
4
2004
Optimally locating a junction point for an underground mine to maximise the net present value. Zbl 1386.90037
Sirinanda, Kashyapa; Brazil, Marcus; Grossman, Peter; Rubinstein, Hyam; Thomas, Doreen
3
2013
Forbidden subpaths for Steiner minimum networks in uniform orientation metrics. Zbl 1014.68119
Brazil, M.; Thomas, D. A.; Weng, J. F.
3
2002
Gradient-constrained minimal Steiner trees. Zbl 0915.05042
Brazil, M.; Thomas, D. A.; Weng, J. F.
3
1998
On the complexity of the Steiner problem. Zbl 1028.90045
Brazil, M.; Thomas, D. A.; Weng, J. F.
3
2000
Stability and active power sharing in droop controlled inverter interfaced microgrids: effect of clock mismatches. Zbl 1400.93008
Kolluri, Ramachandra Rao; Mareels, Iven; Alpcan, Tansu; Brazil, Marcus; de Hoog, Julian; Thomas, Doreen Anne
2
2018
Growth functions for some one-relator monoids. Zbl 0811.20048
Brazil, Marcus
2
1993
Full minimal Steiner trees on lattice sets. Zbl 0874.05018
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
2
1997
Approximating minimum Steiner point trees in Minkowski planes. Zbl 1206.90199
Brazil, M.; Ras, C. J.; Thomas, D. A.
2
2010
Network modelling of underground mine layout: two case studies. Zbl 1156.90476
Thomas, Doreen A.; Brazil, Marcus; Lee, David H.; Wormald, Nicholas C.
2
2007
Gradient-constrained discounted Steiner trees. I: Optimal tree configurations. Zbl 1346.90792
Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A.
2
2016
A geometric characterisation of the quadratic min-power centre. Zbl 1339.90191
Brazil, M.; Ras, C. J.; Thomas, D. A.
2
2014
Flexibility of Steiner trees in uniform orientation metrics. Zbl 1081.05099
Brazil, M.; Winter, P.; Zachariasen, M.
2
2005
Computing skeletons for rectilinearly convex obstacles in the rectilinear plane. Zbl 1442.90035
Volz, Marcus; Brazil, Marcus; Ras, Charl; Thomas, Doreen
1
2020
New pruning rules for the Steiner tree problem and 2-connected Steiner network problem. Zbl 1453.68201
Brazil, Marcus; Volz, Marcus; Zachariasen, Martin; Ras, Charl; Thomas, Doreen
1
2019
Equivalence, indicators, quasi-indicators and optimal Steiner topologies on four points in space. Zbl 1154.90018
Weng, J. F.; MacGregor Smith, J.; Brazil, M.; Thomas, D. A.
1
2008
Rectilinear Steiner minimal trees on parallel lines. Zbl 0944.05020
Brazil, Marcus; Thomas, Doreen A.; Weng, Jia Feng
1
2000
Calculating growth functions for groups using automata. Zbl 0833.20042
Brazil, Marcus
1
1995
Gradient-constrained discounted Steiner trees. II: Optimally locating a discounted Steiner point. Zbl 1336.90099
Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A.
1
2016
Shortest networks on spheres. Zbl 0915.05043
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
1
1998
Optimal curvature and gradient-constrained directional cost paths in 3-space. Zbl 1347.90077
Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A.
1
2015
Optimal curvature-constrained paths for general directional-cost functions. Zbl 1294.90016
Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A.
1
2013
The uniform orientation Steiner tree problem is NP-hard. Zbl 1319.68227
Brazil, Marcus; Zachariasen, Martin
1
2014
Cost optimisation for underground mining networks. Zbl 1093.90067
Brazil, Marcus; Thomas, Doreen A.; Weng, Jia F.; Rubinstein, J. Hyam; Lee, David H.
1
2005
Computing skeletons for rectilinearly convex obstacles in the rectilinear plane. Zbl 1442.90035
Volz, Marcus; Brazil, Marcus; Ras, Charl; Thomas, Doreen
1
2020
New pruning rules for the Steiner tree problem and 2-connected Steiner network problem. Zbl 1453.68201
Brazil, Marcus; Volz, Marcus; Zachariasen, Martin; Ras, Charl; Thomas, Doreen
1
2019
Stability and active power sharing in droop controlled inverter interfaced microgrids: effect of clock mismatches. Zbl 1400.93008
Kolluri, Ramachandra Rao; Mareels, Iven; Alpcan, Tansu; Brazil, Marcus; de Hoog, Julian; Thomas, Doreen Anne
2
2018
Gradient-constrained discounted Steiner trees. I: Optimal tree configurations. Zbl 1346.90792
Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A.
2
2016
Gradient-constrained discounted Steiner trees. II: Optimally locating a discounted Steiner point. Zbl 1336.90099
Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A.
1
2016
Optimal interconnection trees in the plane. Theory, algorithms and applications. Zbl 1319.05044
Brazil, Marcus; Zachariasen, Martin
12
2015
Maximizing the net present value of a Steiner tree. Zbl 1338.90434
Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A.
5
2015
Generalised \(k\)-Steiner tree problems in normed planes. Zbl 1307.68083
Brazil, Marcus; Ras, Charl J.; Swanepoel, Konrad J.; Thomas, Doreen A.
5
2015
Optimal curvature and gradient-constrained directional cost paths in 3-space. Zbl 1347.90077
Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A.
1
2015
On the history of the Euclidean Steiner tree problem. Zbl 1295.05002
Brazil, Marcus; Graham, Ronald L.; Thomas, Doreen A.; Zachariasen, Martin
19
2014
A geometric characterisation of the quadratic min-power centre. Zbl 1339.90191
Brazil, M.; Ras, C. J.; Thomas, D. A.
2
2014
The uniform orientation Steiner tree problem is NP-hard. Zbl 1319.68227
Brazil, Marcus; Zachariasen, Martin
1
2014
Optimally locating a junction point for an underground mine to maximise the net present value. Zbl 1386.90037
Sirinanda, Kashyapa; Brazil, Marcus; Grossman, Peter; Rubinstein, Hyam; Thomas, Doreen
3
2013
Optimal curvature-constrained paths for general directional-cost functions. Zbl 1294.90016
Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A.
1
2013
Curvature-constrained directional-cost paths in the plane. Zbl 1259.49068
Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A.
6
2012
The bottleneck 2-connected \(k\)-Steiner network problem for \(k \leq 2\). Zbl 1243.05064
Brazil, M.; Ras, C. J.; Thomas, D. A.
4
2012
Approximating minimum Steiner point trees in Minkowski planes. Zbl 1206.90199
Brazil, M.; Ras, C. J.; Thomas, D. A.
2
2010
Translational packing of arbitrary polytopes. Zbl 1178.90286
Egeblad, Jens; Nielsen, Benny K.; Brazil, Marcus
12
2009
Steiner trees for fixed orientation metrics. Zbl 1169.90467
Brazil, M.; Zachariasen, M.
7
2009
A novel approach to phylogenetic trees: \(d\)-dimensional geometric Steiner trees. Zbl 1168.92035
Brazil, M.; Thomas, D. A.; Nielsen, B. K.; Winter, P.; Wulff-Nilsen, C.; Zachariasen, M.
6
2009
Gradient-constrained minimum networks. II: Labelled or locally minimal Steiner points. Zbl 1168.90626
Brazil, M.; Thomas, D. A.; Weng, J. F.
6
2008
Equivalence, indicators, quasi-indicators and optimal Steiner topologies on four points in space. Zbl 1154.90018
Weng, J. F.; MacGregor Smith, J.; Brazil, M.; Thomas, D. A.
1
2008
Network optimization for the design of underground mines. Zbl 1131.90410
Brazil, M.; Thomas, D. A.
12
2007
Optimisation in underground mining. Zbl 1189.90088
Alford, Christopher; Brazil, Marcus; Lee, David H.
5
2007
Network modelling of underground mine layout: two case studies. Zbl 1156.90476
Thomas, Doreen A.; Brazil, Marcus; Lee, David H.; Wormald, Nicholas C.
2
2007
Canonical forms and algorithms for Steiner trees in uniform orientation metrics. Zbl 1095.68074
Brazil, M.; Thomas, D. A.; Weng, J. F.; Zachariasen, M.
9
2006
Locally minimal uniformly oriented shortest networks. Zbl 1275.90114
Brazil, Marcus; Thomas, Doreen A.; Weng, Jia Feng
4
2006
Flexibility of Steiner trees in uniform orientation metrics. Zbl 1081.05099
Brazil, M.; Winter, P.; Zachariasen, M.
2
2005
Cost optimisation for underground mining networks. Zbl 1093.90067
Brazil, Marcus; Thomas, Doreen A.; Weng, Jia F.; Rubinstein, J. Hyam; Lee, David H.
1
2005
Upper and lower bounds for the lengths of Steiner trees in 3-space. Zbl 1068.05014
Brazil, M.; Thomas, D. A.; Weng, J. F.
4
2004
Forbidden subpaths for Steiner minimum networks in uniform orientation metrics. Zbl 1014.68119
Brazil, M.; Thomas, D. A.; Weng, J. F.
3
2002
Gradient-constrained minimum networks. I: Fundamentals. Zbl 1068.90605
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
13
2001
Minimum networks in uniform orientation metrics. Zbl 0973.05022
Brazil, M.; Thomas, D. A.; Weng, J. F.
9
2000
On the complexity of the Steiner problem. Zbl 1028.90045
Brazil, M.; Thomas, D. A.; Weng, J. F.
3
2000
Rectilinear Steiner minimal trees on parallel lines. Zbl 0944.05020
Brazil, Marcus; Thomas, Doreen A.; Weng, Jia Feng
1
2000
Gradient-constrained minimal Steiner trees. Zbl 0915.05042
Brazil, M.; Thomas, D. A.; Weng, J. F.
3
1998
Shortest networks on spheres. Zbl 0915.05043
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
1
1998
Minimal Steiner trees for rectangular arrays of lattice points. Zbl 0883.05038
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
5
1997
Full minimal Steiner trees on lattice sets. Zbl 0874.05018
Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
2
1997
Minimal Steiner trees for \(2^ k \times 2^ k\) square lattices. Zbl 0844.05036
Brazil, M.; Cole, T.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C.
4
1996
Calculating growth functions for groups using automata. Zbl 0833.20042
Brazil, Marcus
1
1995
Growth functions for some nonautomatic Baumslag-Solitar groups. Zbl 0804.20027
Brazil, Marcus
11
1994
Maximal subgroups of infinite symmetric groups. Zbl 0795.20002
Brazil, Marcus; Covington, Jacinta; Penttila, Tim; Praeger, Cheryl E.; Woods, Alan R.
6
1994
Growth functions for some one-relator monoids. Zbl 0811.20048
Brazil, Marcus
2
1993
Monoid growth functions for braid groups. Zbl 0789.20036
Brazil, Marcus
6
1991
all top 5

Cited by 200 Authors

35 Thomas, Doreen Anne
34 Brazil, Marcus N.
14 Rubinstein, J. Hyam
13 Ras, Charl J.
13 Weng, Jia Feng
8 Zachariasen, Martin
6 Grossman, Peter Alexander
6 Stoyan, Yuriĭ Grygorovych
5 Swanepoel, Konrad J.
5 Wormald, Nicholas Charles
4 Sirinanda, K. G.
4 Volz, Marcus
4 Winter, Pawel
3 Chugay, Andrey M.
3 East, James
3 Li, Jianping
3 Lichen, Junran
2 Ahn, Hee-Kap
2 Alt, Helmut
2 Bose, Prosenjit K.
2 Catusse, Nicolas
2 Chang, Alan J.
2 D’angelo, Anthony
2 Durocher, Stephane
2 Egeblad, Jens
2 Fampa, Marcia Helena C.
2 Goycoolea, Marcos
2 Lee, David H.
2 Maculan, Nelson F.
2 Mairesse, Jean
2 Mareels, Iven M. Y.
2 Martini, Horst
2 Mitchell, James D.
2 Müller-Hannemann, Matthias
2 Newman, Alexandra M.
2 Nielsen, Benny K.
2 Praeger, Cheryl Elisabeth
2 Prendergast, Kevin H.
2 Renjith, Pazhaniappan
2 Sadagopan, Narasimhan
2 Schneider, Csaba
2 Shapiro, Michael D.
2 Stepanova, E. I.
2 Wang, Wencheng
2 Wulff-Nilsen, Christian
1 Abbes, Samy
1 Adams, Jared
1 Albenque, Marie
1 Almeida, Maria Teresa
1 Alonso, Javier
1 Andersen, Patrick John
1 Andrés-Thió, Nicolau
1 Arkin, Esther M.
1 Astrakhantsev, Lev
1 Avdoshkin, Alexander
1 Ayala, José L.
1 Bae, Sang Won
1 Bailey, Rosemary A.
1 Baird, Paul
1 Banakh, Iryna
1 Banakh, Taras Onufrievich
1 Bannikova, A. G.
1 Bennell, Julia A.
1 Bortfeldt, Andreas
1 Bregman, Corey
1 Buchin, Kevin
1 Caffarelli, Elena A.
1 Cambazard, Hadrien
1 Cameron, Peter Jephson
1 Campeau, Louis-Pierre
1 Carvalho, Filipa D.
1 Cheong, Otfried
1 Chepoi, Victor D.
1 Chinyere, Ihechukwu
1 Choi, Seongjun
1 Ciobanu, Laura
1 de la Harpe, Pierre
1 Dudkin, Fëdor Anatol’evich
1 Dymarsky, Anatoly
1 Efrat, Alon
1 Elder, Murray J.
1 Espinoza, Daniel G.
1 Fardoun, Ali
1 Feldmann, Andreas Emil
1 Ferrari-Trecate, Giancarlo
1 Flores, Alfinio
1 Freden, Eric M.
1 Fung, Wai Shing
1 Gamache, Michel
1 Garavelli, Claudio
1 Garbulińska-Węgrzyn, Joanna
1 Goberna, Miguel Angel
1 Gouëzel, Sébastien
1 Grigorchuk, Rostislav Ivanovich
1 Groves, John R. J.
1 Grune, Ansgar
1 Hale, Trevor S.
1 Halverson, Denise M.
1 Hart, George William
1 Hermiller, Susan M.
...and 100 more Authors
all top 5

Cited in 54 Serials

11 Journal of Global Optimization
9 European Journal of Operational Research
8 Networks
6 Computational Geometry
5 Discrete Applied Mathematics
5 Journal of Algebra
5 Algorithmica
4 Journal of Optimization Theory and Applications
4 Transactions of the American Mathematical Society
3 Geometriae Dedicata
3 Theoretical Computer Science
3 Computers & Operations Research
3 International Journal of Computational Geometry & Applications
3 Cybernetics and Systems Analysis
3 Journal of Mathematical Sciences (New York)
3 International Transactions in Operational Research
3 Journal of Combinatorial Optimization
2 Journal of Combinatorial Theory. Series A
2 Results in Mathematics
2 Graphs and Combinatorics
2 Annals of Operations Research
2 International Journal of Algebra and Computation
2 Computational Optimization and Applications
2 Optimization and Engineering
2 Optimization Letters
1 Communications in Algebra
1 International Journal of Mathematical Education in Science and Technology
1 Information Processing Letters
1 Israel Journal of Mathematics
1 Journal of Mathematical Biology
1 Journal of Geometry and Physics
1 Archiv der Mathematik
1 Automatica
1 Colloquium Mathematicum
1 Journal of Pure and Applied Algebra
1 Mathematische Nachrichten
1 Mathematika
1 Proceedings of the Edinburgh Mathematical Society. Series II
1 Real Analysis Exchange
1 SIAM Journal on Computing
1 Operations Research Letters
1 IMRN. International Mathematics Research Notices
1 Linear Algebra and its Applications
1 European Journal of Control
1 Theory of Computing Systems
1 Nexus Network Journal
1 Journal of Dynamical and Control Systems
1 Journal of High Energy Physics
1 Moscow Mathematical Journal
1 Discrete Optimization
1 Discrete Mathematics, Algorithms and Applications
1 Mathematical Programming Computation
1 Advances in Decision Sciences
1 Journal of Advanced Studies in Topology

Citations by Year