Edit Profile (opens in new tab) Thomas, Doreen Anne Co-Author Distance Author ID: thomas.doreen-anne Published as: Thomas, D. A.; Thomas, Doreen A.; Thomas, Doreen; Thomas, Doreen Anne more...less Homepage: https://findanexpert.unimelb.edu.au/profile/401-doreen-thomas External Links: MGP · ORCID · Wikidata · dblp Documents Indexed: 84 Publications since 1976, including 4 Additional arXiv Preprints Co-Authors: 40 Co-Authors with 82 Joint Publications 829 Co-Co-Authors all top 5 Co-Authors 2 single-authored 58 Brazil, Marcus N. 34 Rubinstein, J. Hyam 28 Weng, Jia Feng 17 Ras, Charl J. 13 Grossman, Peter Alexander 9 Wormald, Nicholas Charles 5 Volz, Marcus 5 Zachariasen, Martin 4 Mareels, Iven M. Y. 4 Sirinanda, K. G. 4 Swanepoel, Konrad J. 4 Whittle, David 3 Burkitt, Anthony N. 3 Chang, Alan J. 3 Gilson, Matthieu 3 Grayden, David B. 3 van Hemmen, J. Leo 2 Andrés-Thió, Nicolau 2 Booth, Ryan S. 2 Cole, Tim J. 2 Kirszenblat, David 2 Lee, David H. 2 Prendergast, Kevin H. 2 Volz, M. G. 2 Weng, Jia 2 Yarmuch, Juan L. 1 Alpcan, Tansu 1 Covington, Jacinta 1 de Hoog, Julian 1 Graham, Ronald Lewis 1 Hendriksen, Michael 1 Kolluri, Ramachandra Rao 1 Lee, Jae 1 Nielsen, Benny K. 1 Payne, Michael S. 1 Sirinanda, Kashyapa 1 Smith, James MacGregor 1 Winter, Pawel 1 Wulff-Nilsen, Christian 1 Xu, G. all top 5 Serials 15 Networks 10 Journal of Global Optimization 4 Journal of Combinatorial Theory. Series A 3 Biological Cybernetics 3 Discrete Applied Mathematics 3 Journal of Optimization Theory and Applications 3 Algorithmica 3 International Transactions in Operational Research 3 Optimization and Engineering 2 Geometriae Dedicata 2 Discrete & Computational Geometry 2 Computers & Operations Research 2 Computational Geometry 2 European Journal of Operational Research 2 Discrete Mathematics, Algorithms and Applications 1 Archive for History of Exact Sciences 1 Journal of Mathematical Biology 1 Beiträge zur Algebra und Geometrie 1 Automatica 1 Journal of Algebra 1 The Quarterly Journal of Mathematics. Oxford Second Series 1 SIAM Journal on Computing 1 Theoretical Computer Science 1 SIAM Journal on Discrete Mathematics 1 Annals of Operations Research 1 International Journal of Computational Geometry & Applications 1 The Australasian Journal of Combinatorics 1 Journal of Combinatorial Optimization 1 Fundamenta Informaticae 1 The ANZIAM Journal 1 Discrete Optimization 1 Optimization Letters all top 5 Fields 49 Operations research, mathematical programming (90-XX) 39 Combinatorics (05-XX) 16 Computer science (68-XX) 5 Biology and other natural sciences (92-XX) 4 Numerical analysis (65-XX) 4 Information and communication theory, circuits (94-XX) 3 Geometry (51-XX) 3 Convex and discrete geometry (52-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 1 Mathematical logic and foundations (03-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 63 Publications have been cited 296 times in 158 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 27 2014 A variational approach to the Steiner network problem. Zbl 0734.05040 Rubinstein, J. H.; Thomas, D. A. 24 1991 The Steiner ratio conjecture for six points. Zbl 0739.05034 Rubinstein, J. H.; Thomas, D. A. 15 1991 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 Network optimization for the design of underground mines. Zbl 1131.90410 Brazil, M.; Thomas, D. A. 11 2007 Steiner trees for terminals constrained to curves. Zbl 0869.05023 Rubinstein, J. H.; Thomas, D. A.; Wormald, N. C. 11 1997 Minimum networks for four points in space. Zbl 1009.05042 Rubinstein, J. H.; Thomas, D. A.; Weng, J. 10 2002 Graham’s problem on shortest networks for points on a circle. Zbl 0748.05051 Rubinstein, J. H.; Thomas, D. A. 9 1992 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 Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I: Input selectivity-strengthening correlated input pathways. Zbl 1342.92018 Gilson, Matthieu; Burkitt, Anthony N.; Grayden, David B.; Thomas, Doreen A.; van Hemmen, J. Leo 9 2009 Minimum networks in uniform orientation metrics. Zbl 0973.05022 Brazil, M.; Thomas, D. A.; Weng, J. F. 9 2000 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. 8 2009 Generalised \(k\)-Steiner tree problems in normed planes. Zbl 1307.68083 Brazil, Marcus; Ras, Charl J.; Swanepoel, Konrad J.; Thomas, Doreen A. 7 2015 Degree-five Steiner points cannot reduce network costs for planar sets. Zbl 0774.05032 Rubinstein, J. H.; Thomas, D. A.; Weng, J. F. 7 1992 The bottleneck 2-connected \(k\)-Steiner network problem for \(k \leq 2\). Zbl 1243.05064 Brazil, M.; Ras, C. J.; Thomas, D. 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. 6 1997 The Steiner ratio conjecture for cocircular points. Zbl 0774.05031 Rubinstein, J. H.; Thomas, D. A. 6 1992 Gradient-constrained minimum networks. II: Labelled or locally minimal Steiner points. Zbl 1168.90626 Brazil, M.; Thomas, D. A.; Weng, J. F. 6 2008 On the complexity of the Steiner problem. Zbl 1028.90045 Brazil, M.; Thomas, D. A.; Weng, J. F. 6 2000 Locally minimal uniformly oriented shortest networks. Zbl 1275.90114 Brazil, Marcus; Thomas, Doreen A.; Weng, Jia Feng 5 2006 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. 5 1996 Curvature-constrained directional-cost paths in the plane. Zbl 1259.49068 Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A. 5 2012 Minimum cost flow-dependent communication networks. Zbl 1103.90031 Thomas, D. A.; Weng, J. F. 4 2006 Solving the prize-collecting Euclidean Steiner tree problem. Zbl 07771166 Whittle, David; Brazil, Marcus; Grossman, Peter A.; Rubinstein, J. Hyam; Thomas, Doreen A. 4 2022 Full minimal Steiner trees on lattice sets. Zbl 0874.05018 Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C. 4 1997 Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II: Input selectivity-symmetry breaking. Zbl 1342.92019 Gilson, Matthieu; Burkitt, Anthony N.; Grayden, David B.; Thomas, Doreen A.; van Hemmen, J. Leo 4 2009 Forbidden subpaths for Steiner minimum networks in uniform orientation metrics. Zbl 1014.68119 Brazil, M.; Thomas, D. A.; Weng, J. F. 3 2002 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. 3 2015 Upper and lower bounds for the lengths of Steiner trees in 3-space. Zbl 1068.05014 Brazil, M.; Thomas, D. A.; Weng, J. F. 3 2004 A polynomial algorithm for a constrained traveling salesman problem. Zbl 0990.90102 Rubinstein, J. H.; Thomas, D. A.; Wormald, N. C. 3 2001 Gradient-constrained minimal Steiner trees. Zbl 0915.05042 Brazil, M.; Thomas, D. A.; Weng, J. F. 3 1998 A geometric characterisation of the quadratic min-power centre. Zbl 1339.90191 Brazil, M.; Ras, C. J.; Thomas, D. A. 3 2014 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 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 Approximating minimum Steiner point trees in Minkowski planes. Zbl 1206.90199 Brazil, M.; Ras, C. J.; Thomas, D. A. 2 2010 Optimum ramp design in open pit mines. Zbl 1458.90678 Yarmuch, Juan L.; Brazil, Marcus; Rubinstein, Hyam; Thomas, Doreen A. 2 2020 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. 2 2016 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 2 2013 Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence. Zbl 1403.92008 Gilson, Matthieu; Burkitt, Anthony N.; Grayden, David B.; Thomas, Doreen A.; van Hemmen, J. Leo 2 2010 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 2 2019 A model for open-pit pushback design with operational constraints. Zbl 1519.90132 Yarmuch, Juan L.; Brazil, Marcus; Rubinstein, Hyam; Thomas, Doreen A. 2 2023 Exactly solvable and unsolvable shortest network problems in 3D-space. Zbl 1062.05037 Booth, R. S.; Thomas, D. A.; Weng, J. F. 1 2004 The Steiner minimal network for convex configurations. Zbl 0774.05033 Thomas, D. A.; Rubinstein, J. H.; Cole, T. 1 1993 Computing Steiner points for gradient-constrained minimum networks. Zbl 1264.05134 Thomas, D. A.; Weng, J. F. 1 2010 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 Rectilinear Steiner minimal trees on parallel lines. Zbl 0944.05020 Brazil, Marcus; Thomas, Doreen A.; Weng, Jia Feng 1 2000 Euclidean Steiner trees optimal with respect to swapping 4-point subtrees. Zbl 1292.90306 Thomas, Doreen A.; Weng, Jia F. 1 2014 Probability Steiner trees and maximum parsimony in phylogenetic analysis. Zbl 1279.92061 Weng, J. F.; Mareels, I.; Thomas, D. A. 1 2012 Computing skeletons for rectilinearly convex obstacles in the rectilinear plane. Zbl 1442.90035 Volz, Marcus; Brazil, Marcus; Ras, Charl; Thomas, Doreen 1 2020 Identifying Steiner minimal trees on four points in space. Zbl 1221.05063 Weng, J. F.; Thomas, D. A.; Mareels, I. 1 2009 Optimum Steiner ratio for gradient-constrained networks connecting three points in 3-space. I. Zbl 1200.90033 Prendergast, K.; Thomas, D. A.; Weng, J. F. 1 2009 Shortest networks on spheres. Zbl 0915.05043 Brazil, M.; Rubinstein, J. H.; Thomas, D. A.; Weng, J. F.; Wormald, N. C. 1 1998 Computing Steiner points and probability Steiner points in \(\ell _{1}\) and \(\ell _{2}\) metric spaces. Zbl 1194.05020 Weng, J. F.; Mareels, I.; Thomas, D. A. 1 2009 An exact algorithm for the bottleneck 2-connected \(k\)-Steiner network problem in \(L_p\) planes. Zbl 1329.05268 Brazil, M.; Ras, C. J.; Thomas, D. A. 1 2016 A flow-dependent quadratic Steiner tree problem in the Euclidean plane. Zbl 1390.90151 Brazil, Marcus N.; Ras, Charl J.; Thomas, Doreen A. 1 2014 Computing minimum 2-edge-connected Steiner networks in the Euclidean plane. Zbl 1407.90091 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 The Gilbert arborescence problem. Zbl 1269.90026 Volz, M. G.; Brazil, M.; Ras, C. J.; Swanepoel, K. J.; Thomas, D. A. 1 2013 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 Minimal curvature-constrained networks. Zbl 1412.90159 Kirszenblat, D.; Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A. 1 2018 Network augmentation for disaster-resilience against geographically correlated failure. Zbl 1530.90029 Andrés-Thió, Nicolau; Brazil, Marcus; Ras, Charl; Thomas, Doreen 1 2023 A model for open-pit pushback design with operational constraints. Zbl 1519.90132 Yarmuch, Juan L.; Brazil, Marcus; Rubinstein, Hyam; Thomas, Doreen A. 2 2023 Network augmentation for disaster-resilience against geographically correlated failure. Zbl 1530.90029 Andrés-Thió, Nicolau; Brazil, Marcus; Ras, Charl; Thomas, Doreen 1 2023 Solving the prize-collecting Euclidean Steiner tree problem. Zbl 07771166 Whittle, David; Brazil, Marcus; Grossman, Peter A.; Rubinstein, J. Hyam; Thomas, Doreen A. 4 2022 Optimum ramp design in open pit mines. Zbl 1458.90678 Yarmuch, Juan L.; Brazil, Marcus; Rubinstein, Hyam; Thomas, Doreen A. 2 2020 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 2 2019 Computing minimum 2-edge-connected Steiner networks in the Euclidean plane. Zbl 1407.90091 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 Minimal curvature-constrained networks. Zbl 1412.90159 Kirszenblat, D.; Sirinanda, K. G.; Brazil, M.; Grossman, P. A.; Rubinstein, J. H.; Thomas, D. A. 1 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. 2 2016 An exact algorithm for the bottleneck 2-connected \(k\)-Steiner network problem in \(L_p\) planes. Zbl 1329.05268 Brazil, M.; Ras, C. J.; Thomas, D. A. 1 2016 Generalised \(k\)-Steiner tree problems in normed planes. Zbl 1307.68083 Brazil, Marcus; Ras, Charl J.; Swanepoel, Konrad J.; Thomas, Doreen A. 7 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. 3 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 27 2014 A geometric characterisation of the quadratic min-power centre. Zbl 1339.90191 Brazil, M.; Ras, C. J.; Thomas, D. A. 3 2014 Euclidean Steiner trees optimal with respect to swapping 4-point subtrees. Zbl 1292.90306 Thomas, Doreen A.; Weng, Jia F. 1 2014 A flow-dependent quadratic Steiner tree problem in the Euclidean plane. Zbl 1390.90151 Brazil, Marcus N.; Ras, Charl J.; Thomas, Doreen A. 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 2 2013 The Gilbert arborescence problem. Zbl 1269.90026 Volz, M. G.; Brazil, M.; Ras, C. J.; Swanepoel, K. J.; Thomas, D. A. 1 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 The bottleneck 2-connected \(k\)-Steiner network problem for \(k \leq 2\). Zbl 1243.05064 Brazil, M.; Ras, C. J.; Thomas, D. A. 6 2012 Curvature-constrained directional-cost paths in the plane. Zbl 1259.49068 Chang, Alan J.; Brazil, Marcus; Rubinstein, J. Hyam; Thomas, Doreen A. 5 2012 Probability Steiner trees and maximum parsimony in phylogenetic analysis. Zbl 1279.92061 Weng, J. F.; Mareels, I.; Thomas, D. A. 1 2012 Approximating minimum Steiner point trees in Minkowski planes. Zbl 1206.90199 Brazil, M.; Ras, C. J.; Thomas, D. A. 2 2010 Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks V: self-organization schemes and weight dependence. Zbl 1403.92008 Gilson, Matthieu; Burkitt, Anthony N.; Grayden, David B.; Thomas, Doreen A.; van Hemmen, J. Leo 2 2010 Computing Steiner points for gradient-constrained minimum networks. Zbl 1264.05134 Thomas, D. A.; Weng, J. F. 1 2010 Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. I: Input selectivity-strengthening correlated input pathways. Zbl 1342.92018 Gilson, Matthieu; Burkitt, Anthony N.; Grayden, David B.; Thomas, Doreen A.; van Hemmen, J. Leo 9 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. 8 2009 Emergence of network structure due to spike-timing-dependent plasticity in recurrent neuronal networks. II: Input selectivity-symmetry breaking. Zbl 1342.92019 Gilson, Matthieu; Burkitt, Anthony N.; Grayden, David B.; Thomas, Doreen A.; van Hemmen, J. Leo 4 2009 Identifying Steiner minimal trees on four points in space. Zbl 1221.05063 Weng, J. F.; Thomas, D. A.; Mareels, I. 1 2009 Optimum Steiner ratio for gradient-constrained networks connecting three points in 3-space. I. Zbl 1200.90033 Prendergast, K.; Thomas, D. A.; Weng, J. F. 1 2009 Computing Steiner points and probability Steiner points in \(\ell _{1}\) and \(\ell _{2}\) metric spaces. Zbl 1194.05020 Weng, J. F.; Mareels, I.; Thomas, D. A. 1 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. 11 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 5 2006 Minimum cost flow-dependent communication networks. Zbl 1103.90031 Thomas, D. A.; Weng, J. F. 4 2006 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. 3 2004 Exactly solvable and unsolvable shortest network problems in 3D-space. Zbl 1062.05037 Booth, R. S.; Thomas, D. A.; Weng, J. F. 1 2004 Minimum networks for four points in space. Zbl 1009.05042 Rubinstein, J. H.; Thomas, D. A.; Weng, J. 10 2002 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 A polynomial algorithm for a constrained traveling salesman problem. Zbl 0990.90102 Rubinstein, J. H.; Thomas, D. A.; Wormald, N. C. 3 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. 6 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 Steiner trees for terminals constrained to curves. Zbl 0869.05023 Rubinstein, J. H.; Thomas, D. A.; Wormald, N. C. 11 1997 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. 6 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. 4 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. 5 1996 The Steiner minimal network for convex configurations. Zbl 0774.05033 Thomas, D. A.; Rubinstein, J. H.; Cole, T. 1 1993 Graham’s problem on shortest networks for points on a circle. Zbl 0748.05051 Rubinstein, J. H.; Thomas, D. A. 9 1992 Degree-five Steiner points cannot reduce network costs for planar sets. Zbl 0774.05032 Rubinstein, J. H.; Thomas, D. A.; Weng, J. F. 7 1992 The Steiner ratio conjecture for cocircular points. Zbl 0774.05031 Rubinstein, J. H.; Thomas, D. A. 6 1992 A variational approach to the Steiner network problem. Zbl 0734.05040 Rubinstein, J. H.; Thomas, D. A. 24 1991 The Steiner ratio conjecture for six points. Zbl 0739.05034 Rubinstein, J. H.; Thomas, D. A. 15 1991 all cited Publications top 5 cited Publications all top 5 Cited by 188 Authors 53 Thomas, Doreen Anne 41 Brazil, Marcus N. 24 Rubinstein, J. Hyam 17 Ras, Charl J. 15 Weng, Jia Feng 9 Grossman, Peter Alexander 8 Zachariasen, Martin 7 Gilson, Matthieu 6 Burkitt, Anthony N. 6 Du, Ding-Zhu 6 Swanepoel, Konrad J. 6 Wormald, Nicholas Charles 5 Grayden, David B. 4 Cole, Tim J. 4 Maculan Filho, Nelson 4 Sirinanda, K. G. 4 van Hemmen, J. Leo 4 Winter, Pawel 3 Mareels, Iven M. Y. 3 Stepanova, E. I. 3 Volz, Marcus 3 Whittle, David 2 Andersen, Patrick John 2 Banakh, Taras Onufrievich 2 Bose, Prosenjit K. 2 Catusse, Nicolas 2 Chang, Alan J. 2 D’angelo, Anthony 2 Durocher, Stephane 2 Fampa, Marcia Helena C. 2 Hwang, Frank Kwangming 2 Il’yutko, Denis Petrovich 2 Ivanov, Aleksandr Olegovich 2 Kirszenblat, David 2 Lee, David H. 2 Li, Jianping 2 Lichen, Junran 2 Müller-Hannemann, Matthias 2 Newman, Alexandra M. 2 Nielsen, Benny K. 2 Nikonov, Igor Mikhailovich 2 Ouzia, Hacene 2 Pinto, Renan Vicente 2 Prendergast, Kevin H. 2 Renjith, Pazhaniappan 2 Sadagopan, Narasimhan 2 Tuzhilin, Alexey Avgustinovich 2 Wang, Wencheng 2 Weng, Jia 2 Yarmuch, Juan L. 2 Zachos, Anastasios N. 2 Zheng, Yujie 1 Almeida, Maria Teresa 1 Amaya, Jorge 1 Andrés-Thió, Nicolau 1 Astrakhantsev, Lev 1 Athreya, Jayadev S. 1 Aulicino, David 1 Avdoshkin, Alexander 1 Ayala, José L. 1 Baird, Paul 1 Banakh, Iryna 1 Bannikova, A. G. 1 Booth, Ryan S. 1 Brányi, Balázs 1 Brydun, Viktoria 1 Buchin, Kevin 1 Bürck, Moritz 1 Cabello, Sergio 1 Caffarelli, Elena A. 1 Cambazard, Hadrien 1 Cano, Rafael G. 1 Carvalho, Filipa D. 1 Çela, Eranda 1 Chepoi, Victor D. 1 Chikin, Vladimir Maksimovich 1 Contreras-Bolton, Carlos 1 de Rezende, Pedro Jussieu 1 de Souza, Cid Carvalho 1 Deĭneko, Vladimir G. 1 Dymarsky, Anatoly 1 Fardoun, Ali 1 Feldmann, Andreas Emil 1 Ferrari-Trecate, Giancarlo 1 Flores, Alfinio 1 Fung, Wai Shing 1 Gajser, David 1 Gambardella, Luca Maria 1 Garbulińska-Węgrzyn, Joanna 1 Goberna, Miguel Angel 1 Goranci, Gramoz 1 Goycoolea, Marcos 1 Graham, Ronald Lewis 1 Gualandi, Stefano 1 Habenschuss, Stefan 1 Hale, Trevor S. 1 Halverson, Denise M. 1 Heijnen, Petra W. 1 Hendriksen, Michael 1 Herder, Paulien M. ...and 88 more Authors all top 5 Cited in 59 Serials 17 Networks 12 Journal of Global Optimization 8 Algorithmica 8 International Transactions in Operational Research 7 Discrete Applied Mathematics 6 Biological Cybernetics 6 European Journal of Operational Research 5 Journal of Combinatorial Theory. Series A 5 Annals of Operations Research 5 Computational Geometry 5 Optimization and Engineering 4 Journal of Optimization Theory and Applications 4 Journal of Mathematical Sciences (New York) 3 Discrete Mathematics, Algorithms and Applications 3 Mathematical Programming Computation 2 Discrete Mathematics 2 International Journal of Mathematical Education in Science and Technology 2 Geometriae Dedicata 2 Graphs and Combinatorics 2 Discrete & Computational Geometry 2 Computers & Operations Research 2 Neural Computation 2 International Journal of Computational Geometry & Applications 2 Sbornik: Mathematics 2 Journal of Combinatorial Optimization 2 Optimization Letters 1 Archive for History of Exact Sciences 1 Bulletin of the Australian Mathematical Society 1 Information Processing Letters 1 Journal of Mathematical Biology 1 Moscow University Mathematics Bulletin 1 Journal of Geometry and Physics 1 Beiträge zur Algebra und Geometrie 1 Automatica 1 Colloquium Mathematicum 1 Mathematika 1 Quaestiones Mathematicae 1 Real Analysis Exchange 1 SIAM Journal on Computing 1 Operations Research Letters 1 Linear Algebra and its Applications 1 Mathematical Programming. Series A. Series B 1 Boletim da Sociedade Brasileira de Matemática. Nova Série 1 Computational Optimization and Applications 1 Top 1 Journal of Computational Neuroscience 1 European Journal of Control 1 Analysis (München) 1 Nexus Network Journal 1 Journal of High Energy Physics 1 SIAM Journal on Applied Dynamical Systems 1 Journal of Statistical Mechanics: Theory and Experiment 1 Networks and Spatial Economics 1 Discrete Optimization 1 Set-Valued and Variational Analysis 1 Journal of the Operations Research Society of China 1 Analysis and Geometry in Metric Spaces 1 Arnold Mathematical Journal 1 CGT. Computing in Geometry and Topology all top 5 Cited in 26 Fields 85 Operations research, mathematical programming (90-XX) 63 Combinatorics (05-XX) 28 Computer science (68-XX) 12 Convex and discrete geometry (52-XX) 12 Biology and other natural sciences (92-XX) 11 Geometry (51-XX) 5 Calculus of variations and optimal control; optimization (49-XX) 5 General topology (54-XX) 5 Numerical analysis (65-XX) 4 Differential geometry (53-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Systems theory; control (93-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Measure and integration (28-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Difference and functional equations (39-XX) 1 Functional analysis (46-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Mechanics of particles and systems (70-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.