A. Y. Alfakih, A. Khandani, and H. Wolkowicz, Solving Euclidean distance matrix completion problems via 594 semidefinite programming, Comput. Optim. Appl, vol.12, pp.13-30, 1999.
DOI : 10.1007/978-1-4615-5197-3_2

URL : http://www.cst.uwaterloo.ca/j/AYCOMP99.pdf

B. Alipanahi, N. Krislock, A. Ghodsi, H. Wolkowicz, L. Donaldson et al., Determining protein 596 structures from NOESY distance constraints by semidefinite programming, J. Comput. Biol, vol.20, pp.296-310
DOI : 10.1089/cmb.2012.0089

URL : https://www.liebertpub.com/doi/pdf/10.1089/cmb.2012.0089

F. C. Almeida, A. H. Moraes, and F. Gomes-neto, An overview on protein structure determination by 599 NMR: historical and future perspectives of the use of distance geometry methods, pp.377-412

H. Berman, J. Westbrook, Z. Feng, G. Gilliland, T. Bhat et al., The 602 Protein Data Bank, Nucl. Acids Res, vol.28, pp.235-242, 2000.

M. Billeter, W. Braun, and K. Wüthrich, Sequential resonance assignments in protein 1 H nuclear magnetic 604 resonance spectra. Computation of sterically allowed proton-proton distances and statistical analysis of 605 proton-proton distances in single crystal protein conformations, J. Mol. Biol, vol.155, p.606, 1982.

P. Biswas, T. Lian, T. Wang, and Y. Ye, Semidefinite programming based algorithms for sensor network 607 localization, ACM Trans. Sens. Netw, vol.2, pp.188-220, 2006.
DOI : 10.1145/1149283.1149286

T. Bizien, D. Durand, P. Roblina, A. Thureau, P. Vachette et al., A brief Survey of State-of-the-Art 609

, BioSAXS. Protein Pept. Lett, vol.23, pp.217-231, 2016.

A. Cassioli, B. Bordeaux, G. Bouvier, A. Mucherino, R. Alves et al., , p.611

T. Malliavin, An algorithm to enumerate all possible protein conformations verifying a set of distance 612 constraints, BMC Bioinform, vol.16, pp.16-23, 2015.

A. Cassioli, O. Gunluk, C. Lavor, and L. Liberti, Discretization vertex orders in distance geometry, Discrete, vol.614
DOI : 10.1016/j.dam.2014.08.035

, Appl. Math, vol.197, pp.27-41, 2015.

Z. A. Chen, A. Jawhari, L. Fischer, C. Buchen, S. Tahir et al., , p.616

L. Bukowski-wills, J. Nilges, M. Cramer, P. Rappsilber, and J. , Architecture of the RNA polymerase, p.617

, II-TFIIF complex revealed by cross-linking and mass spectrometry, EMBO J, vol.29, p.618, 2010.

V. Costa, A. Mucherino, C. Lavor, A. Cassioli, L. M. Carvalho et al., Discretization orders for 619 protein side chains, J. Glob. Optim, vol.60, pp.333-349, 2014.
DOI : 10.1007/s10898-013-0135-1

G. Crippen and T. Havel, Distance Geometry and Molecular Conformation, p.621, 1988.

J. Dattorro, Convex Optimization and Euclidean Distance Geometry, p.622, 2005.

I. Dokmanic, R. Parhizkar, J. Ranieri, and M. Vetterli, Euclidean distance matrices: essential theory, algo-623 rithms, and applications. Sig. Process. Mag, IEEE, vol.32, issue.6, p.624, 2015.
DOI : 10.1109/msp.2015.2398954

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

Q. Dong and Z. Wu, A linear-time algorithm for solving the molecular distance geometry problem with 625 exact inter-atomic distances, J. Glob. Optim, vol.22, p.626, 2002.

Q. Dong and Z. Wu, A geometric build-up algorithm for solving the molecular distance geometry problem 627 with sparse distance data, J. Glob. Optim, vol.26, issue.3, pp.321-333, 2003.

D. Ferguson, A. Marsh, T. Metzger, D. Garrett, and K. Kastella, Conformational searches for the global 629 minimum of protein models, J. Glob. Optim, vol.4, pp.209-227, 1994.

F. Fiorioto, F. Damberger, T. Herrmann, and K. Wüthrich, Automated amino acid side-chain NMR assign-631 ment of proteins using 13C-and 15N-resolved 3D [1H,1H]-NOESY, J. Biomol. NMR, vol.42, p.632, 2008.

D. S. Gonçalves and A. Mucherino, Discretization orders and efficient computation of cartesian coordinates 633 for distance geometry, Optim. Lett, vol.8, pp.2111-2125, 2014.

D. S. Gonçalves, A. Mucherino, and C. Lavor, An adaptive branching scheme for the branch & prune 635 algorithm applied to distance geometry, Workshop on 636 Computational Optimization (WCO14), p.637, 2014.

S. L. Grand and K. Merz, The application of the genetic algorithm to the minimization of potential energy 638 functions, J. Glob. Optim, vol.3, pp.49-66, 1993.

P. Guerry, V. D. Duong, and T. Herrmann, CASD-NMR 2: robust and accurate unsupervised analysis of raw 640 NOESY spectra and protein structure determination with UNIO, J. Biomol. NMR, vol.62, p.641, 2015.

P. Güntert, Automated NMR structure calculation with CYANA, Methods Mol. Biol, vol.278, pp.353-378

T. Herrmann, P. Güntert, and K. Wüthrich, Protein NMR structure determination with automated NOE 644 assignment using the new software CANDID and the torsion angle dynamics algorithm DYANA, J. Mol

, Biol, vol.319, pp.209-227, 2002.

T. Herrmann, P. Güntert, and K. Wüthrich, Protein NMR structure determination with automated NOE-647 identification in the NOESY spectra using the new software ATNOS, J. Biomol. NMR, vol.24, pp.171-189

L. and H. An, Solving large scale molecular distance geometry problems by a smoothing technique via the 650 Gaussian transform and d.c. programming, J. Glob. Optim, vol.27, p.651, 2003.

H. X. Huang, Z. A. Liang, and P. Pardalos, Some properties for the Euclidean distance matrix and positive 652 semidefinite matrix completion problems, J. Glob. Optim, vol.25, p.653, 2003.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimization by simulated annealing, Science, vol.220, pp.671-680

N. Krislock and H. Wolkowicz, Explicit sensor network localization using semidefinite representations and 656 facial reductions, SIAM J. Optim, vol.20, pp.2679-2708, 2010.

C. Lavor, R. Alves, W. Figueiredo, A. Petraglia, and N. Maculan, Clifford algebra and the discretizable 658 molecular distance geometry problem, Adv. Appl. Clifford Algebr, vol.25, p.659, 2015.

C. Lavor, J. Lee, A. L. John, L. Liberti, A. Mucherino et al., Discretization orders for 660 distance geometry problems, Optim. Lett, vol.6, p.661, 2012.

C. Lavor, L. Liberti, N. Maculan, and A. Mucherino, The discretizable molecular distance geometry prob-662 lem, Comput. Optim. Appl, vol.52, pp.115-146, 2012.

C. Lavor, L. Liberti, N. Maculan, and A. Mucherino, Recent advances on the discretizable molecular 664 distance geometry problem, Eur. J. Oper. Res, vol.219, p.665, 2012.

C. Lavor, L. Liberti, and A. Mucherino, The interval branch-and-prune algorithm for the discretizable 666 molecular distance geometry problem with inexact distances, J. Glob. Optim, vol.56, p.667, 2013.

C. Lavor, A. Mucherino, L. Liberti, and N. Maculan, On the computation of protein backbones by using 668 artificial backbones of hydrogens, J. Glob. Optim, vol.50, p.669, 2011.

L. Liberti, C. Lavor, and N. Maculan, A branch-and-prune algorithm for the molecular distance geometry 670 problem, Int. Trans. Oper. Res, vol.15, pp.1-17, 2008.

L. Liberti, C. Lavor, N. Maculan, and F. Marinelli, Double variable neighbourhood search with smoothing 672 for the molecular distance geometry problem, J. Glob. Optim, vol.43, p.673, 2009.

L. Liberti, C. Lavor, N. Maculan, and A. Mucherino, Euclidean distance geometry and applications, SIAM 674 Rev, vol.56, p.675, 2014.
URL : https://hal.archives-ouvertes.fr/hal-01093056

L. Liberti, C. Lavor, A. Mucherino, and N. Maculan, Molecular Distance Geometry Methods: from Con-676 tinuous to Discrete, Int. Trans. Oper. Res, vol.18, p.677, 2011.

L. Liberti, C. Lavor, and A. Mucherino, The discretizable molecular distance geometry problem seems 678 easier on proteins, Distance Geometry, pp.679-726, 2013.

L. Liberti, B. Masson, J. Lee, C. Lavor, and A. Mucherino, On the number of realizations of certain, p.681
URL : https://hal.archives-ouvertes.fr/hal-01093060

, Henneberg graphs arising in protein conformation, Discrete Appl. Math, vol.165, p.682, 2014.

J. P. Linge, M. Habeck, W. Rieping, and M. Nilges, ARIA: automated NOE assignment and NMR structure 683 calculation, Bioinformatics, vol.19, p.684, 2003.

M. Locatelli and F. Schoen, Minimal interatomic distance in morse clusters, J. Glob. Optim, vol.22, issue.1, p.685, 2002.

T. Malliavin, A. Mucherino, and M. Nilges, Distance geometry in structural biology: new perspectives, pp.329-350

A. Man-cho-so and Y. Ye, Theory of semidefinite programming for sensor network localization

, Program. B, vol.109, pp.367-384, 2007.

. Optim, , vol.4, pp.135-170, 1994.

J. Moré and Z. Wu, Distance geometry optimization for protein structures, J. Glob. Optim, vol.15, issue.3, p.693, 1999.

J. Moré and Z. Wu, Distance geometry optimization for protein structures, J. Glob. Optim, vol.15, pp.219-223

A. Mucherino, On the identification of discretization orders for distance geometry with intervals, 697 Proceedings of Geometric Science of Information (GSI13), vol.698, pp.231-238, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00912677

A. Mucherino, A pseudo De Bruijn graph representation for discretization orders for distance geometry
URL : https://hal.archives-ouvertes.fr/hal-01196707

, Proceedings of the 3rd International Work-Conference on Bioinformatics and Biomedical Engineering, vol.701, p.702, 2015.

A. Mucherino, C. Lavor, and L. Liberti, The discretizable distance geometry problem, Optim. Lett, vol.6, pp.1671-1686, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00756943

A. Mucherino, C. Lavor, and L. Liberti, Distance Geometry: Theory, p.705
URL : https://hal.archives-ouvertes.fr/hal-00912679

. Applications and . Springer, , 2013.

A. Mucherino, C. Lavor, T. Malliavin, L. Liberti, M. Nilges et al., Influence of pruning devices 707 on the solution of molecular distance geometry problems, Pro-708 ceedings of the 10th International Symposium on Experimental Algorithms (SEA11), vol.6630, p.5, 2011.

J. Ryu and D. S. Kim, Protein structure optimization by side-chain positioning via beta-complex, J. Glob
DOI : 10.1007/s10898-012-9886-3

, Optim, vol.57, issue.1, pp.217-250, 2013.

R. Santana, P. Larrañaga, and J. Lozano, Side chain placement using estimation of distribution algorithms

, Artif. Intell. Med, vol.39, pp.49-63, 2007.

J. B. Saxe, Embeddability of weighted graphs in k-space is strongly NP-hard, Proceedings of 17th

, Allerton Conference in Communications. Control and Computing, p.716, 1979.

T. Schlick, Molecular Modelling and Simulation: An Interdisciplinary Guide, p.717, 2002.
DOI : 10.1007/978-1-4419-6351-2

I. Schoenberg, Remarks to Maurice Fréchet's article "Sur la définition axiomatique d'une classe d'espaces 718 distanciés vectoriellement applicable sur l'espace de Hilbert, Ann. Math, vol.36, p.719, 1935.
DOI : 10.2307/1968654

M. Sippl and H. Scheraga, Cayley-Menger coordinates, Proc. Natl. Acad. Sci. USA, vol.83, p.720, 1986.
DOI : 10.1073/pnas.83.8.2283

URL : https://www.pnas.org/content/pnas/83/8/2283.full.pdf

A. Sit and Z. Wu, Solving a generalized distance geometry problem for protein structure determination

, Bull. Math. Biol, vol.73, pp.2809-2836, 2011.

M. Souza, C. Lavor, A. Muritiba, and N. Maculan, Solving the molecular distance geometry problem with 723 innacurate distance data, S7), p.6, 2013.
DOI : 10.1186/1471-2105-14-s9-s7

URL : https://doi.org/10.1186/1471-2105-14-s9-s7

H. Thompson, Calculation of cartesian coordinates and their derivatives from internal molecular coordi-725 nates, J. Chem. Phys, vol.47, pp.3407-3410, 1967.

J. Volk, T. Herrmann, and K. Wüthrich, Automated sequence-specific protein NMR assigment using memetic 727 algorithm MATCH, J. Biomol. NMR, vol.41, pp.127-138, 2008.
DOI : 10.1007/s10858-008-9243-5

URL : http://doc.rero.ch/record/317988/files/10858_2008_Article_9243.pdf

D. Wu and Z. Wu, An updated geometric build-up algorithm for solving the molecular distance geometry 729 problem with sparse distance data, J. Glob. Optim, vol.37, p.730, 2007.
DOI : 10.1007/s10898-006-9080-6

D. Wu, Z. Wu, and Y. Yuan, Rigid versus unique determination of protein structures with geometric buildup

, Optim. Lett, vol.2, pp.319-331, 2008.

K. Wüthrich, M. Billeter, and W. Braun, Pseudo-structures for the 20 common amino acids for use in 733 studies of protein conformations by measurements of intramolecular proton-proton distance constraints 734 with Nuclear Magnetic Ressonance, J. Mol. Biol, vol.169, p.735, 1983.

Y. Zhang and J. Skolnick, TM-align: a protein structure alignment algorithm based on TM-score

, Acids Res, vol.33, pp.2302-2309, 2005.

Z. Zou, R. Bird, and R. Schnabel, A stochastic/perturbation global optimization algorithm for distance 738 geometry problems, J. Glob. Optim, vol.11, issue.1, pp.91-105, 1997.