T. Achterberg, SCIP: solving constraint integer programs, Mathematical Programming Computation, vol.29, issue.2, pp.1-41, 2009.
DOI : 10.1007/s12532-008-0001-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.374.7376

A. Ahmadi and G. Hall, Sum of squares basis pursuit with linear and second order cone programming, 2016.
DOI : 10.1090/conm/685/13712

A. Abdo-alfakih, H. Khandani, and . Wolkowicz, Solving Euclidean Distance Matrix Completion Problems Via Semidefinite Programming, In: Computational Optimization and Applications, vol.121, pp.13-30, 1999.
DOI : 10.1007/978-1-4615-5197-3_2

F. Alizadeh, Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization, SIAM Journal on Optimization, vol.5, issue.1, pp.13-51, 1995.
DOI : 10.1137/0805002

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.4131

M. Anjos and J. Lasserre, Handbook on semidefinite, conic and polynomial optimization. First edition International Series in Operations Research and Management Science, 2012.
DOI : 10.1007/978-1-4614-0769-0_1

M. Aps, What if the solver stalls?, 2014.

M. Aps, The MOSEK command line tool. Version 7.1 (Revision 60), 2016.

C. Audet, P. Hansen, B. Jaumard, and G. Savard, Links Between Linear Bilevel and Mixed 0???1 Programming Problems, Journal of Optimization Theory and Applications, vol.19, issue.2, pp.273-300, 1997.
DOI : 10.1023/A:1022645805569

H. Berman, K. Henrick, and H. Nakamura, Announcing the worldwide Protein Data Bank, Nature Structural Biology, vol.10, issue.12, p.980, 2003.
DOI : 10.1038/nsb1203-980

J. Berstel and L. Boasson, Context-free Languages In: Handbook of Theoretical Computer Science, van Leeuwen, pp.59-102, 1990.

L. Blumenthal, Theory and Applications of Distance Geometry, 1953.

W. Bofill and J. Gomez, LINEAR AND NONLINEAR SEMIDEFINITE PROGRAMMING, Pesquisa Operacional, vol.34, issue.3, pp.495-520, 2014.
DOI : 10.1590/0101-7438.2014.034.03.0495

URL : http://doi.org/10.1590/0101-7438.2014.034.03.0495

I. Bomze, M. Budinich, P. Pardalos, and M. Pelillo, The Maximum Clique Problem, Supp. A, pp.1-74, 1998.
DOI : 10.1007/978-1-4757-3023-4_1

S. Boyd and L. Vandenberghe, Convex Optimization. First edition, 2004.

M. Brazil, R. Graham, D. Thomas, and M. Zachariasen, On the history of the Euclidean Steiner tree problem, Archive for History of Exact Sciences, vol.30, issue.1, pp.327-354, 2014.
DOI : 10.1007/s00407-013-0127-z

A. Clark, Elements of Abstract Algebra, 1984.

J. Conway, Y. Jiao, and S. Torquato, New family of tilings of three-dimensional Euclidean space by tetrahedra and octahedra, Proceedings of the National Academy of Sciences, vol.105, issue.7257, pp.27-11009, 2011.
DOI : 10.1038/nature08239

A. Costa, P. Hansen, and L. Liberti, Formulation symmetries in circle packing, Proceedings of the 1st International Symposium on Combinatorial Optimization, pp.1303-1310, 2010.
DOI : 10.1016/j.endm.2010.05.165

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.155.2505

A. Costa, P. Hansen, and L. Liberti, On the impact of symmetry-breaking constraints on spatial Branch-and-Bound for circle packing in a square, Discrete Applied Mathematics, vol.161, issue.1-2, pp.1-2, 2013.
DOI : 10.1016/j.dam.2012.07.020

D. Claudia, . Ambrosio, C. Vu-khac-ky, L. Lavor, N. Liberti et al., Computational experience on distance geometry problems 2.0, Proceedings of the XIII Global Optimization Workshop. Ed. by Leocadio Casado, Eligius Hendrix, and Inmaculada Garcia, pp.101-104, 2014.

D. Claudia, M. Ambrosio, J. Fampa, S. Lee, and . Vigerske, On a Nonconvex MINLP Formulation of the Euclidean Steiner Tree Problem in n-Space, Proceedings of the 14th International Symposium on Experimental Algorithms, pp.122-133, 2015.

G. Dias and L. Liberti, Orbital Independence in Symmetric Mathematical Programs, Proceedings of the 9th Annual International Conference on Combinatorial Optimization and Applications, pp.467-480, 2015.
DOI : 10.1007/978-3-319-26626-8_34

G. Dias and L. Liberti, Diagonally Dominant Programming in Distance Geometry, Proceedings of the 4th International Symposium on Combinatorial Optimazation. Ed. by Raffaele Cerulli, Satoru Fujishige, and Ridha Mahjoub, pp.225-236, 2016.
DOI : 10.1007/978-3-319-45587-7_20

G. Dias, L. Liberti, and N. Maculan, Modelling Rank Constraints in Mathematical Programming In: Proceedings of the 13th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, pp.193-196, 2015.

I. Dokmanic, R. Parhizkar, J. Ranieri, and M. Vetterli, Euclidean Distance Matrices: Essential theory, algorithms, and applications, IEEE Signal Processing Magazine, vol.32, issue.6, 2015.
DOI : 10.1109/MSP.2015.2398954

URL : http://arxiv.org/abs/1502.07541

M. Fampa, J. Lee, and N. Maculan, An overview of exact algorithms for the Euclidean Steiner tree problem in nspace, In: International Transactions in Operational Research, vol.235, pp.861-874, 2016.

M. Fampa, J. Lee, and W. Melo, A specialized branchand-bound algorithm for the Euclidean Steiner tree problem in n-space, In: Computational Optimization and Applications, vol.651, pp.47-71, 2016.

M. Fampa and N. Maculan, Using a Conic Formulation for Finding Steiner Minimal Trees, Numerical Algorithms, vol.35, issue.2-4, pp.315-330, 2004.
DOI : 10.1023/B:NUMA.0000021765.17831.bc

M. Fischetti and L. Liberti, Orbital Shrinking, Proceedings of the 2nd International Symposium on Combinatorial Optimization, pp.48-58, 2012.
DOI : 10.1007/978-3-642-32147-4_6

B. Rosiane-de-freitas, N. Dias, J. Maculan, and . Szwarcfiter, Distance geometry approach for special graph coloring problems, 2016.

S. Galli, Parsing AMPL internal format for linear and non-linear expressions. B.Sc. dissertation, DEI, 2004.

M. Garey, R. Graham, and D. Johnson, The Complexity of Computing Steiner Minimal Trees, SIAM Journal on Applied Mathematics, vol.32, issue.4, pp.835-859, 1977.
DOI : 10.1137/0132072

G. Guennebaud and B. Jacob, Eigen -a C++ template library for linear algebra Bounds on eigenvalues of real and complex interval matrices, In: Applied Mathematics and Computation, vol.219, pp.10-5584, 2013.

F. Hwang, D. Richards, and P. Winter, The Steiner Tree Problem. 1st, Annals of Discrete Mathematics, vol.53, 1992.

V. Kaibel and M. Pfetsch, Packing and partitioning orbitopes, Mathematical Programming, vol.2, issue.4, pp.1-36, 2008.
DOI : 10.1007/s10107-006-0081-5

URL : http://arxiv.org/abs/math/0603678

D. Knuth, The Art of Computer Programming, Part II: Seminumerical Algorithms. 1st, 1981.

G. Kochenberger, J. Hao, F. Glover, M. Lewis, Z. Lü et al., The unconstrained binary quadratic programming problem: a survey, Journal of Combinatorial Optimization, vol.52, issue.3, pp.58-81, 2014.
DOI : 10.1007/s10878-014-9734-0

C. Lavor, L. Liberti, and N. Maculan, Computational Experience with the Molecular Distance Geometry Problem, pp.213-225, 2006.
DOI : 10.1007/0-387-30927-6_9

C. Lavor, L. Liberti, N. Maculan, and A. Mucherino, Recent advances on the Discretizable Molecular Distance Geometry Problem, European Journal of Operational Research, vol.219, issue.3, pp.698-706, 2012.
DOI : 10.1016/j.ejor.2011.11.007

URL : https://hal.archives-ouvertes.fr/hal-00756942

C. Lavor, L. Liberti, N. Maculan, and A. Mucherino, The discretizable molecular distance geometry problem, Computational Optimization and Applications, vol.11, issue.3, pp.115-146, 2012.
DOI : 10.1007/s10589-011-9402-6

URL : https://hal.archives-ouvertes.fr/hal-00756940

D. Li, X. Sun, S. Gu, J. Gao, and C. Liu, Polynomially Solvable Cases of Binary Quadratic Programs, Altannar Chinchuluun, pp.199-225, 2010.
DOI : 10.1007/978-0-387-89496-6_11

L. Liberti, Writing Global Optimization Software, pp.211-262, 2006.
DOI : 10.1007/0-387-30528-9_8

L. Liberti, Reformulations in Mathematical Programming: Definitions and Systematics, RAIRO - Operations Research, vol.43, issue.1, pp.55-86, 2009.
DOI : 10.1051/ro/2009005

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.144.2599

L. Liberti, Reformulations in mathematical programming: automatic symmetry detection and exploitation, Mathematical Programming, vol.174, issue.10, pp.273-304, 2012.
DOI : 10.1007/s10107-010-0351-0

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.205.9305

L. Liberti, Symmetry in Mathematical Programming, pp.263-286, 2012.
DOI : 10.1007/978-1-4614-1927-3_9

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.191.589

L. Liberti, S. Cafieri, and D. Savourey, The Reformulation-Optimization Software Engine, Mathematical Software. Ed. by K. Fukuda, J. van der Hoeven, M. Joswig, and N. Takayama
DOI : 10.1007/978-3-642-15582-6_50

URL : https://hal.archives-ouvertes.fr/hal-00979214

L. Liberti, S. Cafieri, and F. Tarissan, Reformulations in Mathematical Programming: A Computational Approach In: Foundations of Computational Intelligence Volume 3: Global Optimization, pp.153-234, 2009.

L. Liberti, C. Lavor, and N. Maculan, A branchand-prune algorithm for the molecular distance geometry problem, In: International Transactions in Operational Research, vol.151, pp.1-17, 2008.

L. Liberti, N. Maculan, and Y. Zhang, Optimal configuration of gamma ray machine radiosurgery units: the sphere covering subproblem, Optimization Letters, vol.114, issue.3, pp.109-121, 2009.
DOI : 10.1007/s11590-008-0095-4

L. Liberti and J. Ostrowski, Stabilizer-based symmetry breaking constraints for mathematical programs, Journal of Global Optimization, vol.47, issue.10, pp.183-194, 2014.
DOI : 10.1007/s10898-013-0106-6

L. Liberti, C. Lavor, N. Maculan, and M. A. Nascimento, Reformulation in mathematical programming: An application to quantum chemistry, Discrete Applied Mathematics, vol.157, issue.6, pp.1309-1318, 2009.
DOI : 10.1016/j.dam.2007.08.044

URL : http://doi.org/10.1016/j.dam.2007.08.044

L. Liberti, C. Lavor, A. Mucherino, and N. Maculan, Molecular distance geometry methods: from continuous to discrete, International Transactions in Operational Research, vol.43, issue.3, pp.33-51, 2010.
DOI : 10.1111/j.1475-3995.2009.00757.x

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.158.3143

L. Liberti, C. Lavor, N. Maculan, and A. Mucherino, Euclidean Distance Geometry and Applications, SIAM Review, vol.56, issue.1, pp.3-69, 2014.
DOI : 10.1137/120875909

URL : https://hal.archives-ouvertes.fr/hal-01093056

N. Maculan, P. Michelon, and A. Xavier, The Euclidean Steiner tree problem in Rn: A mathematical programming formulation, In: Annals of Operations Research, vol.961, pp.209-220, 2000.

F. Margot, Pruning by isomorphism in branch-and-cut, Mathematical Programming, vol.94, issue.1, pp.71-90, 2002.
DOI : 10.1007/s10107-002-0358-2

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.23.3603

F. Margot, Exploiting orbits in symmetric ILP, Mathematical Programming, vol.98, issue.1-3, pp.3-21, 2003.
DOI : 10.1007/s10107-003-0394-6

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.215.3513

F. Margot, Symmetry in Integer Linear Programming, pp.647-681, 2010.
DOI : 10.1007/978-3-540-68279-0_17

B. Mccarl, McCarl GAMS user's guide. GAMS Development Corporation

B. Mckay, Practical graph isomorphism, II, Journal of Symbolic Computation, vol.60, pp.45-87, 1981.
DOI : 10.1016/j.jsc.2013.09.003

B. Mckay and A. Piperno, Practical graph isomorphism, II, Journal of Symbolic Computation, vol.60, pp.94-112, 2014.
DOI : 10.1016/j.jsc.2013.09.003

L. Mencarelli, Y. Sahraoui, and L. Liberti, A multiplicative weights update algorithm for MINLP, EURO Journal on Computational Optimization, vol.174, issue.1
DOI : 10.1007/s13675-016-0069-8

J. Moré and Z. Wu, Distance geometry optimization for protein structures, Journal of Global Optimization, vol.15, issue.3, pp.219-234, 1999.
DOI : 10.1023/A:1008380219900

A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, Distance Geometry: Theory, Methods and Applications, 2013.
DOI : 10.1007/978-1-4614-5128-0

URL : https://hal.archives-ouvertes.fr/hal-00912679

A. F. Roberto-do-nascimento, L. Macambira, R. Cabral, and . Pinto, The discrete ellipsoid covering problem: A discrete geometric programming approach, Discrete Applied Mathematics, vol.164, pp.276-285, 2014.
DOI : 10.1016/j.dam.2012.10.016

A. Neumaier, Molecular Modeling of Proteins and Mathematical Prediction of Protein Structure, SIAM Review, vol.39, issue.3, pp.407-460, 1997.
DOI : 10.1137/S0036144594278060

J. Ostrowski, J. Linderoth, F. Rossi, and S. Smriglio, Orbital Branching, Proceedings of the 1st Conference on Integer Programming and Combinatorial Optimization, pp.104-118, 2007.
DOI : 10.1007/978-3-540-72792-7_9

J. Ostrowski, J. Linderoth, F. Rossi, and S. Smriglio, Constraint Orbital Branching, Proceedings of the 2nd Conference on Integer Programming and Combinatorial Optimization, pp.225-239, 2008.
DOI : 10.1007/978-3-540-68891-4_16

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.410.4294

M. Pfetsch and T. Rehn, A Computational Comparison of Symmetry Handling Methods for Mixed Integer Programs, 2015.

A. Phillips and J. Rosen, A quadratic assignment formulation of the molecular conformation problem, Journal of Global Optimization, vol.2, issue.2, pp.229-241, 1994.
DOI : 10.1007/BF01096724

R. Rosenthal, GAMS -A user's guide. GAMS Development Corporation

J. Rubinstein, D. Thomas, and N. Wormald, Steiner Trees for Terminals Constrained to Curves, SIAM Journal on Discrete Mathematics, vol.10, issue.1, pp.1-17, 1997.
DOI : 10.1137/S0895480192241190

G. Sagnol, Picos -A Python Interface to Conic Optimization Solvers

N. Sahinidis, BARON 14.4.0: Global Optimization of Mixed- Integer Nonlinear Programs -User's manual, 2014.

D. Salvagnin, Orbital Shrinking: A New Tool for Hybrid MIP/CP Methods, Lecture Notes in Computer Science. Berlin, vol.7874, pp.204-215, 2013.
DOI : 10.1007/978-3-642-38171-3_14

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.572.374

D. Salvagnin and T. Walsh, A Hybrid MIP/CP Approach for Multi-activity Shift Scheduling, Ed. by Michela Milano. Lecture Notes in Computer Science. Berlin, vol.7514, pp.633-646, 2012.
DOI : 10.1007/978-3-642-33558-7_46

J. Saxe, Embeddability of weighted graphs in k-space is strongly NP-hard, Proceedings of 17th Allerton Conference in Communications, Control and Computing, pp.480-489, 1979.

H. Sherali, Personal communication, 2007.

A. Singer, Angular synchronization by eigenvectors and semidefinite programming, Applied and Computational Harmonic Analysis, vol.30, issue.1, pp.20-36, 2011.
DOI : 10.1016/j.acha.2010.02.001

URL : http://doi.org/10.1016/j.acha.2010.02.001

W. Smith, How to find Steiner minimal trees in euclideand-space, Algorithmica, vol.15, issue.1, pp.137-177, 1992.
DOI : 10.1007/BF01758756

A. Man, -. So, and Y. Ye, Theory of semidefinite programming for sensor network localization, In: Mathematical Programming B, vol.109, pp.2-3, 2007.

M. Tawarmalani and N. Sahinidis, A polyhedral branchand-cut approach to global optimization, In: Mathematical Programming, vol.103, issue.2, 2005.
DOI : 10.1007/s10107-005-0581-8

G. The and . Group, GAP -Groups, Algorithms and Programming. Version 4, 2014.

L. Vandenberghe and S. Boyd, Semidefinite Programming, SIAM Review, vol.38, issue.1, pp.49-95, 1996.
DOI : 10.1137/1038003

D. Warme, P. Winter, and M. Zachariasen, Exact Algorithms for Plane Steiner Tree Problems: A Computational Study In: Advances in Steiner Trees, pp.81-116, 2000.

P. Winter and M. Zachariasen, Euclidean Steiner minimum trees: An improved exact algorithm, pp.149-166, 1997.
DOI : 10.1002/(sici)1097-0037(199710)30:3<149::aid-net1>3.3.co;2-m

H. Wolkowicz, R. Saigal, and L. Vandenberghe, Handbook of semidefinite programming: Theory, Algorithms and Applications . 1st, International Series in Operations Research and Management Science, 2000.
DOI : 10.1007/978-1-4615-4381-7

G. Xue and Y. Ye, An Efficient Algorithm for Minimizing a Sum of Euclidean Norms with Applications, SIAM Journal on Optimization, vol.7, issue.4, pp.1017-1036, 1997.
DOI : 10.1137/S1052623495288362

Y. Yajima, Positive semidefinite relaxations for distance geometry problems, Japan Journal of Industrial and Applied Mathematics, vol.11, issue.1, pp.87-112, 2002.
DOI : 10.1007/BF03167449

Y. Yemini, The positioning problem -a draft of an intermediate summary, Proceedings of the Conference on Distributed Sensor Networks, pp.137-145, 1978.