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Volumn 56, Issue 1, 2014, Pages 3-69

Euclidean distance geometry and applications

Author keywords

Bar and joint framework; Graph rigidity; Inverse problem; Matrix completion; Protein conformation; Sensor network

Indexed keywords

BAR-AND-JOINT FRAMEWORK; EUCLIDEAN DISTANCE; EUCLIDEAN GEOMETRY; EUCLIDEAN SPACES; INPUT DATAS; MATRIX COMPLETION; MOLECULAR CONFORMATION; PROTEIN CONFORMATION;

EID: 84893837430     PISSN: 00361445     EISSN: None     Source Type: Journal    
DOI: 10.1137/120875909     Document Type: Article
Times cited : (446)

References (245)
  • 2
    • 0002740666 scopus 로고    scopus 로고
    • Solving Euclidean distance matrix completion problems via semidefinite programming
    • A. Alfakih, A. Khandani, and H. Wolkowicz, Solving Euclidean distance matrix completion problems via semidefinite programming, Comput. Optim. Appl., 12 (1999), pp. 13-30.
    • (1999) Comput. Optim. Appl. , vol.12 , pp. 13-30
    • Alfakih, A.1    Khandani, A.2    Wolkowicz, H.3
  • 3
    • 84893821668 scopus 로고    scopus 로고
    • Adaptive branching in iBP with Clifford algebra
    • A. Andrioni, C. Lavor, L. Liberti, A. Mucherino, N. Maculan, and R. Rodriguez, eds., Universidade Federal do Amazonas, Manaus
    • R. Alves, A. Cassioli, A. Mucherino, C. Lavor, and L. Liberti, Adaptive branching in iBP with Clifford algebra, in Proceedings of the Workshop on Distance Geometry and Applications, A. Andrioni, C. Lavor, L. Liberti, A. Mucherino, N. Maculan, and R. Rodriguez, eds., Universidade Federal do Amazonas, Manaus, 2013, pp. 65-69.
    • (2013) Proceedings of the Workshop on Distance Geometry and Applications , pp. 65-69
    • Alves, R.1    Cassioli, A.2    Mucherino, A.3    Lavor, C.4    Liberti, L.5
  • 5
    • 0000067485 scopus 로고
    • Was Euclid an unnecessarily sophisticated psychologist?
    • P. Arabie, Was Euclid an unnecessarily sophisticated psychologist?, Psychometrika, 56 (1991), pp. 567-587.
    • (1991) Psychometrika , vol.56 , pp. 567-587
    • Arabie, P.1
  • 7
    • 0018444223 scopus 로고
    • The rigidity of graphs II
    • L. Asimow and B. Roth, The rigidity of graphs II, J. Math. Anal. Appl., 68 (1979), pp. 171-190.
    • (1979) J. Math. Anal. Appl. , vol.68 , pp. 171-190
    • Asimow, L.1    Roth, B.2
  • 9
    • 35048871074 scopus 로고    scopus 로고
    • On the computational complexity of sensor network localization
    • S. Nikoletseas and J. Rolim, eds., Lecture Notes in Comput. Sci. 3121, Springer, Berlin
    • J. Aspnes, D. Goldenberg, and R. Yang, On the computational complexity of sensor network localization, in Algorithmic Aspects of Wireless Sensor Networks, S. Nikoletseas and J. Rolim, eds., Lecture Notes in Comput. Sci. 3121, Springer, Berlin, 2004, pp. 32-44.
    • (2004) Algorithmic Aspects of Wireless Sensor Networks , pp. 32-44
    • Aspnes, J.1    Goldenberg, D.2    Yang, R.3
  • 11
    • 65949120423 scopus 로고    scopus 로고
    • Cooperative localization for autonomous underwater vehicles
    • A. Bahr, J. Leonard, and M. Fallon, Cooperative localization for autonomous underwater vehicles, Internat. J. Robotics Res., 28 (2009), pp. 714-728.
    • (2009) Internat. J. Robotics Res. , vol.28 , pp. 714-728
    • Bahr, A.1    Leonard, J.2    Fallon, M.3
  • 12
    • 51249170448 scopus 로고
    • Problems of distance geometry and convex properties of quadratic maps
    • A. Barvinok, Problems of distance geometry and convex properties of quadratic maps, Discrete Comput. Geom., 13 (1995), pp. 189-202.
    • (1995) Discrete Comput. Geom. , vol.13 , pp. 189-202
    • Barvinok, A.1
  • 13
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • M. Belkin and P. Niyogi, Laplacian eigenmaps for dimensionality reduction and data representation, Neural Comput., 15 (2003), pp. 1373-1396.
    • (2003) Neural Comput. , vol.15 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 17
    • 0037615148 scopus 로고    scopus 로고
    • Reconstructing a three-dimensional model with arbitrary errors
    • B. Berger, J. Kleinberg, and T. Leighton, Reconstructing a three-dimensional model with arbitrary errors, J. ACM, 46 (1999), pp. 212-235.
    • (1999) J. ACM , vol.46 , pp. 212-235
    • Berger, B.1    Kleinberg, J.2    Leighton, T.3
  • 19
    • 0004242420 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • N. Biggs, Algebraic Graph Theory, Cambridge University Press, Cambridge, UK, 1974.
    • (1974) Algebraic Graph Theory
    • Biggs, N.1
  • 22
    • 33746874045 scopus 로고    scopus 로고
    • Semidefinite programming based algorithms for sensor network localization
    • P. Biswas, T. Lian, T. Wang, and Y. Ye, Semidefinite programming based algorithms for sensor network localization, ACM Trans. Sensor Networks, 2 (2006), pp. 188-220.
    • (2006) ACM Trans. Sensor Networks , vol.2 , pp. 188-220
    • Biswas, P.1    Lian, T.2    Wang, T.3    Ye, Y.4
  • 23
    • 33750083077 scopus 로고    scopus 로고
    • Semidefinite programming approaches for sensor network localization with noisy distance measurements
    • P. Biswas, T.-C. Liang, K.-C. Toh, T.-C. Wang, and Y. Ye, Semidefinite programming approaches for sensor network localization with noisy distance measurements, IEEE Trans. Automation Sci. Engrg., 3 (2006), pp. 360-371.
    • (2006) IEEE Trans. Automation Sci. Engrg. , vol.3 , pp. 360-371
    • Biswas, P.1    Liang, T.-C.2    Toh, K.-C.3    Wang, T.-C.4    Ye, Y.5
  • 24
    • 55549138762 scopus 로고    scopus 로고
    • A distributed SDP approach for large-scale noisy anchorfree graph realization with applications to molecular conformation
    • P. Biswas, K.-C. Toh, and Y. Ye, A distributed SDP approach for large-scale noisy anchorfree graph realization with applications to molecular conformation, SIAM J. Sci. Comput., 30 (2008), pp. 1251-1277.
    • (2008) SIAM J. Sci. Comput. , vol.30 , pp. 1251-1277
    • Biswas, P.1    Toh, K.-C.2    Ye, Y.3
  • 26
    • 34547494898 scopus 로고    scopus 로고
    • A distributed method for solving semidefinite programs arising from ad hoc wireless sensor network localization
    • W. Hager et al., eds., Nonconvex Optim. Appl. 82, Springer, New York
    • P. Biswas and Y. Ye, A distributed method for solving semidefinite programs arising from ad hoc wireless sensor network localization, in Multiscale Optimization Methods and Applications, W. Hager et al., eds., Nonconvex Optim. Appl. 82, Springer, New York, 2006, pp. 69-84.
    • (2006) Multiscale Optimization Methods and Applications , pp. 69-84
    • Biswas, P.1    Ye, Y.2
  • 30
    • 0043010687 scopus 로고
    • On the coordinatization of oriented matroids
    • J. Bokowski and B. Sturmfels, On the coordinatization of oriented matroids, Discrete Comput. Geom., 1 (1986), pp. 293-306.
    • (1986) Discrete Comput. Geom. , vol.1 , pp. 293-306
    • Bokowski, J.1    Sturmfels, B.2
  • 33
    • 0013173620 scopus 로고    scopus 로고
    • Unit disk graph recognition is NP-hard
    • H. Breu and D. Kirkpatrick, Unit disk graph recognition is NP-hard, Comput. Geom., 9 (1998), pp. 3-24.
    • (1998) Comput. Geom. , vol.9 , pp. 3-24
    • Breu, H.1    Kirkpatrick, D.2
  • 34
    • 0001880366 scopus 로고    scopus 로고
    • A subdivision-based algorithm for the sparse resultant
    • J. Canny and I. Emiris, A subdivision-based algorithm for the sparse resultant, J. ACM, 47 (2000), pp. 417-451.
    • (2000) J. ACM , vol.47 , pp. 417-451
    • Canny, J.1    Emiris, I.2
  • 35
    • 34250499792 scopus 로고
    • Analysis of individual differences in multidimensional scaling via an n-way generalization of "eckart-Young" decomposition
    • J. Carroll and J. Chang, Analysis of individual differences in multidimensional scaling via an n-way generalization of "Eckart-Young" decomposition, Psychometrika, 35 (1970), pp. 283-319.
    • (1970) Psychometrika , vol.35 , pp. 283-319
    • Carroll, J.1    Chang, J.2
  • 36
    • 52049122134 scopus 로고    scopus 로고
    • Extending the geometric build-up algorithm for the molecular distance geometry problem
    • R. Carvalho, C. Lavor, and F. Protti, Extending the geometric build-up algorithm for the molecular distance geometry problem, Inform. Process. Lett., 108 (2008), pp. 234-237.
    • (2008) Inform. Process. Lett. , vol.108 , pp. 234-237
    • Carvalho, R.1    Lavor, C.2    Protti, F.3
  • 37
    • 0001997277 scopus 로고
    • Sur les polygones et les polyèdres
    • A.-L. Cauchy, Sur les polygones et les polyèdres, J. Ecole Polytechnique, 16 (1813), pp. 87-99.
    • (1813) J. Ecole Polytechnique , vol.16 , pp. 87-99
    • Cauchy, A.-L.1
  • 38
    • 0039219582 scopus 로고
    • A theorem in the geometry of position
    • A. Cayley, A theorem in the geometry of position, Cambridge Math. J., 2 (1841), pp. 267-271.
    • (1841) Cambridge Math. J. , vol.2 , pp. 267-271
    • Cayley, A.1
  • 42
    • 0024351231 scopus 로고
    • Determination of three-dimensional structures of proteins and nucleic acids in solution by nuclear magnetic resonance spectroscopy
    • G. Clore and A. Gronenborn, Determination of three-dimensional structures of proteins and nucleic acids in solution by nuclear magnetic resonance spectroscopy, Critical Reviews in Biochemistry and Molecular Biology, 24 (1989), pp. 479-564.
    • (1989) Critical Reviews in Biochemistry and Molecular Biology , vol.24 , pp. 479-564
    • Clore, G.1    Gronenborn, A.2
  • 43
    • 51249186858 scopus 로고
    • A counterexample to the rigidity conjecture for polyhedra
    • R. Connelly, A counterexample to the rigidity conjecture for polyhedra, Inst. Hautes Études Sci. Publ. Math., 47 (1978), pp. 333-338.
    • (1978) Inst. Hautes Études Sci. Publ. Math. , vol.47 , pp. 333-338
    • Connelly, R.1
  • 45
    • 17444406687 scopus 로고    scopus 로고
    • Generic global rigidity
    • R. Connelly, Generic global rigidity, Discrete Comput. Geom., 33 (2005), pp. 549-563.
    • (2005) Discrete Comput. Geom. , vol.33 , pp. 549-563
    • Connelly, R.1
  • 46
  • 47
    • 14044262230 scopus 로고    scopus 로고
    • Reliable computation of the points of intersection of n spheres in Rn
    • I. Coope, Reliable computation of the points of intersection of n spheres in Rn, Aust. N. Z. Indust. Appl. Math. J., 42 (2000), pp. C461-C477.
    • (2000) Aust. N. Z. Indust. Appl. Math. J. , vol.42
    • Coope, I.1
  • 51
    • 84893859684 scopus 로고    scopus 로고
    • Distance geometry for realistic molecular conformations
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York
    • G. Crippen, Distance geometry for realistic molecular conformations, in Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York, 2013, pp. 315-328.
    • (2013) Distance Geometry: Theory, Methods, and Applications , pp. 315-328
    • Crippen, G.1
  • 53
    • 84887577976 scopus 로고
    • On the theory of isomeric compounds
    • A. Crum Brown, On the theory of isomeric compounds, Trans. Roy. Soc. Edinburgh, 23 (1864), pp. 707-719.
    • (1864) Trans. Roy. Soc. Edinburgh , vol.23 , pp. 707-719
    • Crum Brown, A.1
  • 54
    • 84866413054 scopus 로고    scopus 로고
    • Sensor network localization by eigenvector synchronization over the Euclidean group
    • M. Cucuringu, Y. Lipman, and A. Singer, Sensor network localization by eigenvector synchronization over the Euclidean group, ACM Trans. Sensor Networks, 8 (2012), pp. 1-42.
    • (2012) ACM Trans. Sensor Networks , vol.8 , pp. 1-42
    • Cucuringu, M.1    Lipman, Y.2    Singer, A.3
  • 55
    • 84892391966 scopus 로고    scopus 로고
    • Eigenvector synchronization, graph rigidity and the molecule problem
    • M. Cucuringu, A. Singer, and D. Cowburn, Eigenvector synchronization, graph rigidity and the molecule problem, Inform. Inference, 1 (2012), pp. 21-67.
    • (2012) Inform. Inference , vol.1 , pp. 21-67
    • Cucuringu, M.1    Singer, A.2    Cowburn, D.3
  • 57
    • 41549152026 scopus 로고    scopus 로고
    • Equality relating Euclidean distance cone to positive semidefinite cone
    • J. Dattorro, Equality relating Euclidean distance cone to positive semidefinite cone, Linear Algebra Appl., 428 (2008), pp. 2597-2600.
    • (2008) Linear Algebra Appl. , vol.428 , pp. 2597-2600
    • Dattorro, J.1
  • 58
  • 65
    • 31244436296 scopus 로고    scopus 로고
    • A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances
    • Q. Dong and Z. Wu, A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances, J. Global Optim., 22 (2002), pp. 365-375.
    • (2002) J. Global Optim. , vol.22 , pp. 365-375
    • Dong, Q.1    Wu, Z.2
  • 66
    • 84867962761 scopus 로고    scopus 로고
    • A geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data
    • Q. Dong and Z. Wu, A geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data, J. Global Optim., 26 (2003), pp. 321-333.
    • (2003) J. Global Optim. , vol.26 , pp. 321-333
    • Dong, Q.1    Wu, Z.2
  • 67
    • 0343402093 scopus 로고
    • Distance geometry and geometric algebra
    • A. Dress and T. Havel, Distance geometry and geometric algebra, Found. Phys., 23 (1993), pp. 1357-1374.
    • (1993) Found. Phys. , vol.23 , pp. 1357-1374
    • Dress, A.1    Havel, T.2
  • 69
    • 33746340255 scopus 로고    scopus 로고
    • Reconstructing distances among objects from their discriminability
    • E. Dzhafarov and H. Colonius, Reconstructing distances among objects from their discriminability, Psychometrika, 71 (2006), pp. 365-386.
    • (2006) Psychometrika , vol.71 , pp. 365-386
    • Dzhafarov, E.1    Colonius, H.2
  • 71
    • 0000802374 scopus 로고
    • The approximation of one matrix by another of lower rank
    • C. Eckart and G. Young, The approximation of one matrix by another of lower rank, Psychometrika, 1 (1936), pp. 211-218.
    • (1936) Psychometrika , vol.1 , pp. 211-218
    • Eckart, C.1    Young, G.2
  • 72
    • 3042551103 scopus 로고    scopus 로고
    • Computer algebra methods for studying and computing molecular conformations
    • I. Emiris and B. Mourrain, Computer algebra methods for studying and computing molecular conformations, Algorithmica, 25 (1999), pp. 372-402.
    • (1999) Algorithmica , vol.25 , pp. 372-402
    • Emiris, I.1    Mourrain, B.2
  • 76
    • 75649092864 scopus 로고    scopus 로고
    • Uniquely localizable networks with few anchors
    • S. Nikoletseas and J. Rolim, eds., Lecture Notes in Comput. Sci. 4240, Springer, Berlin
    • Z. Fekete and T. Jordán, Uniquely localizable networks with few anchors, in Algorithmic Aspects of Wireless Sensor Networks, S. Nikoletseas and J. Rolim, eds., Lecture Notes in Comput. Sci. 4240, Springer, Berlin, 2006, pp. 176-183.
    • (2006) Algorithmic Aspects of Wireless Sensor Networks , pp. 176-183
    • Fekete, Z.1    Jordán, T.2
  • 77
    • 0028422189 scopus 로고
    • The challenges of mobile computing
    • G. Forman and J. Zahorjan, The challenges of mobile computing, IEEE Comput., 27 (1994), pp. 38-47.
    • (1994) IEEE Comput. , vol.27 , pp. 38-47
    • Forman, G.1    Zahorjan, J.2
  • 78
    • 0031125088 scopus 로고    scopus 로고
    • A graph-constructive approach to solving systems of geometric constraints
    • I. Fudos and C. Hoffmann, A graph-constructive approach to solving systems of geometric constraints, ACM Trans. Graphics, 16 (1997), pp. 179-216.
    • (1997) ACM Trans. Graphics , vol.16 , pp. 179-216
    • Fudos, I.1    Hoffmann, C.2
  • 80
    • 0013605370 scopus 로고    scopus 로고
    • Energy minimization of rigid-geometry polypeptides with exactly closed disulfide loops
    • K. Gibson and H. Scheraga, Energy minimization of rigid-geometry polypeptides with exactly closed disulfide loops, J. Comput. Chem., 18 (1997), pp. 403-415.
    • (1997) J. Comput. Chem. , vol.18 , pp. 403-415
    • Gibson, K.1    Scheraga, H.2
  • 81
    • 0001114105 scopus 로고
    • Almost all simply connected closed surfaces are rigid
    • A. Dold and B. Eckmann, eds., Lecture Notes in Math. 438, Springer, Berlin
    • H. Gluck, Almost all simply connected closed surfaces are rigid, in Geometric Topology, A. Dold and B. Eckmann, eds., Lecture Notes in Math. 438, Springer, Berlin, 1975, pp. 225-239.
    • (1975) Geometric Topology , pp. 225-239
    • Gluck, H.1
  • 82
    • 0000771519 scopus 로고
    • An alternating projection algorithm for computing the nearest Euclidean distance matrix
    • W. Glunt, T. L. Hayden, S. Hong, and J. Wells, An alternating projection algorithm for computing the nearest Euclidean distance matrix, SIAM J. Matrix Anal. Appl., 11 (1990), pp. 589-600.
    • (1990) SIAM J. Matrix Anal. Appl. , vol.11 , pp. 589-600
    • Glunt, W.1    Hayden, T.L.2    Hong, S.3    Wells, J.4
  • 83
    • 77955871459 scopus 로고    scopus 로고
    • Characterizing generic global rigidity
    • S. Gortler, A. Healy, and D. Thurston, Characterizing generic global rigidity, Amer. J. Math., 132 (2010), pp. 897-939.
    • (2010) Amer. J. Math. , vol.132 , pp. 897-939
    • Gortler, S.1    Healy, A.2    Thurston, D.3
  • 84
    • 0000071395 scopus 로고
    • Some distance properties of latent root and vector methods in multivariate analysis
    • J. Gower, Some distance properties of latent root and vector methods in multivariate analysis, Biometrika, 53 (1966), pp. 325-338.
    • (1966) Biometrika , vol.53 , pp. 325-338
    • Gower, J.1
  • 85
    • 0009245040 scopus 로고
    • Euclidean distance geometry
    • J. Gower, Euclidean distance geometry, Math. Sci., 7 (1982), pp. 1-14.
    • (1982) Math. Sci. , vol.7 , pp. 1-14
    • Gower, J.1
  • 87
    • 0009407349 scopus 로고
    • Rigidity matroids
    • J. Graver, Rigidity matroids, SIAM J. Discrete Math., 4 (1991), pp. 355-368.
    • (1991) SIAM J. Discrete Math. , vol.4 , pp. 355-368
    • Graver, J.1
  • 89
    • 0033904057 scopus 로고    scopus 로고
    • On the convergence of the block nonlinear Gauss-Seidel method under convex constraints
    • L. Grippo and M. Sciandrone, On the convergence of the block nonlinear Gauss-Seidel method under convex constraints, Oper. Res. Lett., 26 (2000), pp. 127-136.
    • (2000) Oper. Res. Lett. , vol.26 , pp. 127-136
    • Grippo, L.1    Sciandrone, M.2
  • 90
    • 47849109874 scopus 로고
    • Positive definite completions of partial Hermitian matrices
    • R. Grone, C. Johnson, E. de Sá, and H. Wolkowicz, Positive definite completions of partial Hermitian matrices, Linear Algebra Appl., 58 (1984), pp. 109-124.
    • (1984) Linear Algebra Appl. , vol.58 , pp. 109-124
    • Grone, R.1    Johnson, C.2    De Sá, E.3    Wolkowicz, H.4
  • 91
    • 67449096625 scopus 로고    scopus 로고
    • Solving molecular distance geometry problems by global optimization algorithms
    • A. Grosso, M. Locatelli, and F. Schoen, Solving molecular distance geometry problems by global optimization algorithms, Comput. Optim. Appl., 43 (2009), pp. 23-27.
    • (2009) Comput. Optim. Appl. , vol.43 , pp. 23-27
    • Grosso, A.1    Locatelli, M.2    Schoen, F.3
  • 92
    • 84893871115 scopus 로고    scopus 로고
    • Metric matrix embedding in protein structure calculations
    • T. Havel, Metric matrix embedding in protein structure calculations, Magnetic Resonance Chem., 41 (2003), pp. 537-550.
    • (2003) Magnetic Resonance Chem. , vol.41 , pp. 537-550
    • Havel, T.1
  • 93
    • 49049123546 scopus 로고
    • The theory and practice of distance geometry
    • T. Havel, I. Kuntz, and G. Crippen, The theory and practice of distance geometry, Bull. Math. Biol., 45 (1983), pp. 665-720.
    • (1983) Bull. Math. Biol. , vol.45 , pp. 665-720
    • Havel, T.1    Kuntz, I.2    Crippen, G.3
  • 94
    • 0026821495 scopus 로고
    • Conditions for unique graph realizations
    • B. Hendrickson, Conditions for unique graph realizations, SIAM J. Comput., 21 (1992), pp. 65-84.
    • (1992) SIAM J. Comput. , vol.21 , pp. 65-84
    • Hendrickson, B.1
  • 95
    • 0013558430 scopus 로고
    • The molecule problem: Exploiting structure in global optimization
    • B. Hendrickson, The molecule problem: Exploiting structure in global optimization, SIAM J. Optim., 5 (1995), pp. 835-857.
    • (1995) SIAM J. Optim. , vol.5 , pp. 835-857
    • Hendrickson, B.1
  • 98
    • 0242485191 scopus 로고    scopus 로고
    • Solving large scale molecular distance geometry problems by a smoothing technique via the Gaussian transform and D.C. Programming
    • L. Hoai An, Solving large scale molecular distance geometry problems by a smoothing technique via the Gaussian transform and D.C. programming, J. Global Optim., 27 (2003), pp. 375-397.
    • (2003) J. Global Optim. , vol.27 , pp. 375-397
    • Hoai An, L.1
  • 99
    • 1542380919 scopus 로고    scopus 로고
    • Large-scale molecular optimization from distance matrices by a d.c. Optimization approach
    • L. T. Hoai An and P. Dinh Tao, Large-scale molecular optimization from distance matrices by a d.c. optimization approach, SIAM J. Optim., 14 (2003), pp. 77-114.
    • (2003) SIAM J. Optim. , vol.14 , pp. 77-114
    • Hoai An, L.T.1    Dinh Tao, P.2
  • 100
    • 84867966586 scopus 로고    scopus 로고
    • Some properties for the Euclidean distance matrix and positive semidefinite matrix completion problems
    • H.-X. Huang, Z.-A. Liang, and P. Pardalos, Some properties for the Euclidean distance matrix and positive semidefinite matrix completion problems, J. Global Optim., 25 (2003), pp. 3-21.
    • (2003) J. Global Optim. , vol.25 , pp. 3-21
    • Huang, H.-X.1    Liang, Z.-A.2    Pardalos, P.3
  • 102
    • 33751234960 scopus 로고    scopus 로고
    • A distance geometry heuristic for expanding the range of geometries sampled during conformational search
    • S. Izrailev, F. Zhu, and D. Agrafiotis, A distance geometry heuristic for expanding the range of geometries sampled during conformational search, J. Comput. Chem., 26 (2006), pp. 1962-1969.
    • (2006) J. Comput. Chem. , vol.26 , pp. 1962-1969
    • Izrailev, S.1    Zhu, F.2    Agrafiotis, D.3
  • 103
    • 15444370051 scopus 로고    scopus 로고
    • Connected rigidity matroids and unique realization of graphs
    • B. Jackson and T. Jordán, Connected rigidity matroids and unique realization of graphs, J. Combin. Theory Ser. B, 94 (2005), pp. 1-29.
    • (2005) J. Combin. Theory Ser. B , vol.94 , pp. 1-29
    • Jackson, B.1    Jordán, T.2
  • 104
    • 65749094851 scopus 로고    scopus 로고
    • On the rigidity of molecular graphs
    • B. Jackson and T. Jordán, On the rigidity of molecular graphs, Combinatorica, 28 (2008), pp. 645-658.
    • (2008) Combinatorica , vol.28 , pp. 645-658
    • Jackson, B.1    Jordán, T.2
  • 106
    • 0031999150 scopus 로고    scopus 로고
    • An interior-point method for approximate positive semidefinite completions
    • C. Johnson, B. Kroschel, and H. Wolkowicz, An interior-point method for approximate positive semidefinite completions, Comput. Optim. Appl., 9 (1998), pp. 175-190.
    • (1998) Comput. Optim. Appl. , vol.9 , pp. 175-190
    • Johnson, C.1    Kroschel, B.2    Wolkowicz, H.3
  • 108
    • 0026156982 scopus 로고
    • Diffusion equation method of global minimization: Performance for standard test functions
    • J. Kostrowicki and L. Piela, Diffusion equation method of global minimization: Performance for standard test functions, J. Optim. Theory Appl., 69 (1991), pp. 269-284.
    • (1991) J. Optim. Theory Appl. , vol.69 , pp. 269-284
    • Kostrowicki, J.1    Piela, L.2
  • 111
    • 77956091432 scopus 로고    scopus 로고
    • Explicit sensor network localization using semidefinite representations and facial reductions
    • N. Krislock and H. Wolkowicz, Explicit sensor network localization using semidefinite representations and facial reductions, SIAM J. Optim., 20 (2010), pp. 2679-2708.
    • (2010) SIAM J. Optim. , vol.20 , pp. 2679-2708
    • Krislock, N.1    Wolkowicz, H.2
  • 112
    • 0041654220 scopus 로고
    • Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis
    • J. Kruskal, Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis, Psychometrika, 29 (1964), pp. 1-27.
    • (1964) Psychometrika , vol.29 , pp. 1-27
    • Kruskal, J.1
  • 113
    • 24944533365 scopus 로고
    • Nonmetric multidimensional scaling: A numerical method
    • J. Kruskal, Nonmetric multidimensional scaling: A numerical method, Psychometrika, 29 (1964), pp. 115-129.
    • (1964) Psychometrika , vol.29 , pp. 115-129
    • Kruskal, J.1
  • 115
    • 24044443193 scopus 로고    scopus 로고
    • Application of deterministic low-discrepancy sequences in global optimization
    • S. Kucherenko and Y. Sytsko, Application of deterministic low-discrepancy sequences in global optimization, Comput. Optim. Appl., 30 (2004), pp. 297-318.
    • (2004) Comput. Optim. Appl. , vol.30 , pp. 297-318
    • Kucherenko, S.1    Sytsko, Y.2
  • 116
    • 0014856102 scopus 로고
    • On graphs and rigidity of plane skeletal structures
    • G. Laman, On graphs and rigidity of plane skeletal structures, J. Engrg. Math., 4 (1970), pp. 331-340.
    • (1970) J. Engrg. Math. , vol.4 , pp. 331-340
    • Laman, G.1
  • 117
    • 0000160366 scopus 로고    scopus 로고
    • Cuts, matrix completions and graph rigidity
    • M. Laurent, Cuts, matrix completions and graph rigidity, Math. Program., 79 (1997), pp. 255-283.
    • (1997) Math. Program. , vol.79 , pp. 255-283
    • Laurent, M.1
  • 118
    • 0035219189 scopus 로고    scopus 로고
    • Polynomial instances of the positive semidefinite and Euclidean distance matrix completion problems
    • M. Laurent, Polynomial instances of the positive semidefinite and Euclidean distance matrix completion problems, SIAM J. Matrix Anal. Appl., 22 (2000), pp. 874-894.
    • (2000) SIAM J. Matrix Anal. Appl. , vol.22 , pp. 874-894
    • Laurent, M.1
  • 119
    • 3042743084 scopus 로고    scopus 로고
    • Matrix completion problems
    • 2nd ed., C. Floudas and P. Pardalos, eds., Springer, New York
    • M. Laurent, Matrix completion problems, in Encyclopedia of Optimization, 2nd ed., C. Floudas and P. Pardalos, eds., Springer, New York, 2009, pp. 1967-1975.
    • (2009) Encyclopedia of Optimization , pp. 1967-1975
    • Laurent, M.1
  • 120
    • 72949101175 scopus 로고    scopus 로고
    • On generating instances for the molecular distance geometry problem
    • L. Liberti and N.Maculan, eds., Springer, Berlin
    • C. Lavor, On generating instances for the molecular distance geometry problem, in Global Optimization: From Theory to Implementation, L. Liberti and N.Maculan, eds., Springer, Berlin, 2006, pp. 405-414.
    • (2006) Global Optimization: From Theory to Implementation , pp. 405-414
    • Lavor, C.1
  • 123
    • 59449086627 scopus 로고    scopus 로고
    • Computational experience with the molecular distance geometry problem
    • J. Pintér, ed., Springer, Berlin
    • C. Lavor, L. Liberti, and N. Maculan, Computational experience with the molecular distance geometry problem, in Global Optimization: Scientific and Engineering Case Studies, J. Pintér, ed., Springer, Berlin, 2006, pp. 213-225.
    • (2006) Global Optimization: Scientific and Engineering Case Studies , pp. 213-225
    • Lavor, C.1    Liberti, L.2    Maculan, N.3
  • 125
    • 72749085157 scopus 로고    scopus 로고
    • Molecular distance geometry problem
    • 2nd ed., C. Floudas and P. Pardalos, eds., Springer, New York
    • C. Lavor, L. Liberti, and N. Maculan, Molecular distance geometry problem, in Encyclopedia of Optimization, 2nd ed., C. Floudas and P. Pardalos, eds., Springer, New York, 2009, pp. 2305-2311.
    • (2009) Encyclopedia of Optimization , pp. 2305-2311
    • Lavor, C.1    Liberti, L.2    Maculan, N.3
  • 126
    • 84863580995 scopus 로고    scopus 로고
    • A note on "a Branch-and-Prune Algorithm for the Molecular Distance Geometry Problem"
    • C. Lavor, L. Liberti, and N. Maculan, A note on "A Branch-and-Prune Algorithm for the Molecular Distance Geometry Problem," Internat. Trans. Oper. Res., 18 (2011), pp. 751-752.
    • (2011) Internat. Trans. Oper. Res. , vol.18 , pp. 751-752
    • Lavor, C.1    Liberti, L.2    Maculan, N.3
  • 128
    • 84857919606 scopus 로고    scopus 로고
    • Recent advances on the discretizable molecular distance geometry problem
    • C. Lavor, L. Liberti, N. Maculan, and A. Mucherino, Recent advances on the discretizable molecular distance geometry problem, European J. Oper. Res., 219 (2012), pp. 698-706.
    • (2012) European J. Oper. Res. , vol.219 , pp. 698-706
    • Lavor, C.1    Liberti, L.2    Maculan, N.3    Mucherino, A.4
  • 129
    • 84879688166 scopus 로고    scopus 로고
    • The interval branch-and-prune algorithm for the discretizable molecular distance geometry problem with inexact distances
    • C. Lavor, L. Liberti, and A. Mucherino, The interval branch-and-prune algorithm for the discretizable molecular distance geometry problem with inexact distances, J. Global Optim., 56 (2013), pp. 855-871.
    • (2013) J. Global Optim. , vol.56 , pp. 855-871
    • Lavor, C.1    Liberti, L.2    Mucherino, A.3
  • 133
    • 78149264118 scopus 로고    scopus 로고
    • Discrete approaches for solving molecular distance geometry problems using NMR data
    • C. Lavor, A. Mucherino, L. Liberti, and N. Maculan, Discrete approaches for solving molecular distance geometry problems using NMR data, Internat. J. Comput. Biosci., 1 (2010), pp. 88-94.
    • (2010) Internat. J. Comput. Biosci. , vol.1 , pp. 88-94
    • Lavor, C.1    Mucherino, A.2    Liberti, L.3    Maculan, N.4
  • 135
    • 79955868839 scopus 로고    scopus 로고
    • On the computation of protein backbones by using artificial backbones of hydrogens
    • C. Lavor, A. Mucherino, L. Liberti, and N. Maculan, On the computation of protein backbones by using artificial backbones of hydrogens, J. Global Optim., 50 (2011), pp. 329-344.
    • (2011) J. Global Optim. , vol.50 , pp. 329-344
    • Lavor, C.1    Mucherino, A.2    Liberti, L.3    Maculan, N.4
  • 136
    • 84893869775 scopus 로고    scopus 로고
    • Finding low-energy homopolymer conformations by a discrete approach
    • D. Aloise, P. Hansen, and C. Rocha, eds., Universidade Federal do Rio Grande do Norte, Natal
    • C. Lavor, A. Mucherino, L. Liberti, and N. Maculan, Finding low-energy homopolymer conformations by a discrete approach, in Proceedings of the Global Optimization Workshop, D. Aloise, P. Hansen, and C. Rocha, eds., Universidade Federal do Rio Grande do Norte, Natal, 2012.
    • (2012) Proceedings of the Global Optimization Workshop
    • Lavor, C.1    Mucherino, A.2    Liberti, L.3    Maculan, N.4
  • 137
    • 0346895023 scopus 로고    scopus 로고
    • The effect of distance-cutoff on the performance of the distance matrix error when used as a potential function to drive conformational search
    • H. Bohr and S. Brunak, eds., CRC Press, Boca Raton, FL
    • S. Le Grand, A. Elofsson, and D. Eisenberg, The effect of distance-cutoff on the performance of the distance matrix error when used as a potential function to drive conformational search, in Protein Folds: A Distance Based Approach, H. Bohr and S. Brunak, eds., CRC Press, Boca Raton, FL, 1996, pp. 105-113.
    • (1996) Protein Folds: A Distance Based Approach , pp. 105-113
    • Le Grand, S.1    Elofsson, A.2    Eisenberg, D.3
  • 139
    • 84860821487 scopus 로고    scopus 로고
    • An SDP-based divide-and-conquer algorithm for large-scale noisy anchor-free graph realization
    • N.-H. Z. Leung and K.-C. Toh, An SDP-based divide-and-conquer algorithm for large-scale noisy anchor-free graph realization, SIAM J. Sci. Comput., 31 (2009), pp. 4351-4372.
    • (2009) SIAM J. Sci. Comput. , vol.31 , pp. 4351-4372
    • Leung, N.-H.Z.1    Toh, K.-C.2
  • 141
    • 59149103712 scopus 로고    scopus 로고
    • Reformulations in mathematical programming: Definitions and systematics
    • L. Liberti, Reformulations in mathematical programming: Definitions and systematics, RAIRO Oper. Res., 43 (2009), pp. 55-85.
    • (2009) RAIRO Oper. Res. , vol.43 , pp. 55-85
    • Liberti, L.1
  • 142
  • 144
    • 84883341082 scopus 로고    scopus 로고
    • On a relationship between graph realizability and distance matrix completion
    • A. Migdalas, A. Sifaleras, C. Georgiadis, J. Papathanaiou, and E. Stiakakis, eds., Proc. Math. Statist. 31, Springer, Berlin
    • L. Liberti and C. Lavor, On a relationship between graph realizability and distance matrix completion, in Optimization Theory, Decision Making, and Operational Research Applications, A. Migdalas, A. Sifaleras, C. Georgiadis, J. Papathanaiou, and E. Stiakakis, eds., Proc. Math. Statist. 31, Springer, Berlin, 2013, pp. 39-48.
    • (2013) Optimization Theory, Decision Making, and Operational Research Applications , pp. 39-48
    • Liberti, L.1    Lavor, C.2
  • 145
    • 68949155001 scopus 로고    scopus 로고
    • A branch-and-prune algorithm for the molecular distance geometry problem
    • L. Liberti, C. Lavor, and N. Maculan, A branch-and-prune algorithm for the molecular distance geometry problem, Internat. Trans. Oper. Res., 15 (2008), pp. 1-17.
    • (2008) Internat. Trans. Oper. Res. , vol.15 , pp. 1-17
    • Liberti, L.1    Lavor, C.2    Maculan, N.3
  • 146
    • 59449085654 scopus 로고    scopus 로고
    • Double variable neighbourhood search with smoothing for the molecular distance geometry problem
    • L. Liberti, C. Lavor, N. Maculan, and F. Marinelli, Double variable neighbourhood search with smoothing for the molecular distance geometry problem, J. Global Optim., 43 (2009), pp. 207-218.
    • (2009) J. Global Optim. , vol.43 , pp. 207-218
    • Liberti, L.1    Lavor, C.2    Maculan, N.3    Marinelli, F.4
  • 147
    • 84884931980 scopus 로고    scopus 로고
    • The discretizable molecular distance geometry problem seems easier on proteins
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York
    • L. Liberti, C. Lavor, and A. Mucherino, The discretizable molecular distance geometry problem seems easier on proteins, in Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York, 2013, pp. 47-60.
    • (2013) Distance Geometry: Theory, Methods, and Applications , pp. 47-60
    • Liberti, L.1    Lavor, C.2    Mucherino, A.3
  • 150
    • 84855991185 scopus 로고    scopus 로고
    • Branch-and-prune trees with bounded width
    • G. Nicosia and A. Pacifici, eds., Università di Roma 2-Tor Vergata, Rome
    • L. Liberti, B. Masson, C. Lavor, and A. Mucherino, Branch-and-prune trees with bounded width, in Proceedings of Cologne/Twente Workshop, G. Nicosia and A. Pacifici, eds., Università di Roma 2-Tor Vergata, Rome, 2011.
    • (2011) Proceedings of Cologne/Twente Workshop
    • Liberti, L.1    Masson, B.2    Lavor, C.3    Mucherino, A.4
  • 152
    • 84884925574 scopus 로고    scopus 로고
    • On the number of realizations of certain Henneberg graphs arising in protein conformation
    • to appear
    • L. Liberti, B. Masson, J. Lee, C. Lavor, and A. Mucherino, On the number of realizations of certain Henneberg graphs arising in protein conformation, Discrete Appl. Math., to appear.
    • Discrete Appl. Math.
    • Liberti, L.1    Masson, B.2    Lee, J.3    Lavor, C.4    Mucherino, A.5
  • 153
    • 27744485554 scopus 로고    scopus 로고
    • Centre for Process Systems Engineering, Chemical Engineering Department, Imperial College London, London
    • L. Liberti, P. Tsiakis, B. Keeping, and C. Pantelides, ooOPS, Centre for Process Systems Engineering, Chemical Engineering Department, Imperial College London, London, 2001.
    • (2001) OoOPS
    • Liberti, L.1    Tsiakis, P.2    Keeping, B.3    Pantelides, C.4
  • 156
    • 84907590286 scopus 로고    scopus 로고
    • Distance geometry in structural biology
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York
    • T. Malliavin, A. Mucherino, and M. Nilges, Distance geometry in structural biology, in Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York, 2013, pp. 329-350.
    • (2013) Distance Geometry: Theory, Methods, and Applications , pp. 329-350
    • Malliavin, T.1    Mucherino, A.2    Nilges, M.3
  • 157
    • 33846661142 scopus 로고    scopus 로고
    • Theory of semidefinite programming for sensor network localization
    • A. Man-Cho So and Y. Ye, Theory of semidefinite programming for sensor network localization, Math. Program. Ser. B, 109 (2007), pp. 367-384.
    • (2007) Math. Program. Ser. B , vol.109 , pp. 367-384
    • Man-Cho So, A.1    Ye, Y.2
  • 158
    • 0028517404 scopus 로고
    • Efficient inverse kinematics for general 6R manipulators
    • D. Manocha and J. Canny, Efficient inverse kinematics for general 6R manipulators, IEEE Trans. Robotics Automation, 10 (1994), pp. 648-657.
    • (1994) IEEE Trans. Robotics Automation , vol.10 , pp. 648-657
    • Manocha, D.1    Canny, J.2
  • 159
    • 0001766634 scopus 로고
    • On reciprocal figures and diagrams of forces
    • J. Maxwell, On reciprocal figures and diagrams of forces, Philos. Mag., 27 (1864), pp. 250-261.
    • (1864) Philos. Mag. , vol.27 , pp. 250-261
    • Maxwell, J.1
  • 160
    • 0001766636 scopus 로고
    • On the calculation of the equilibrium and stiffness of frames
    • J. Maxwell, On the calculation of the equilibrium and stiffness of frames, Philos. Mag., 27 (1864), pp. 294-299.
    • (1864) Philos. Mag. , vol.27 , pp. 294-299
    • Maxwell, J.1
  • 161
    • 0002418040 scopus 로고
    • Untersuchungen über allgemeine Metrik
    • K. Menger, Untersuchungen über allgemeine Metrik, Math. Ann., 100 (1928), pp. 75-163.
    • (1928) Math. Ann. , vol.100 , pp. 75-163
    • Menger, K.1
  • 162
    • 0040167690 scopus 로고
    • New foundation of Euclidean geometry
    • K. Menger, New foundation of Euclidean geometry, Amer. J. Math., 53 (1931), pp. 721-745.
    • (1931) Amer. J. Math. , vol.53 , pp. 721-745
    • Menger, K.1
  • 163
    • 0042385969 scopus 로고    scopus 로고
    • Computational real algebraic geometry
    • 2nd ed., J. Goodman and J. O'Rourke, eds., CRC Press, Boca Raton, FL
    • B. Mishra, Computational real algebraic geometry, in Handbook of Discrete and Computational Geometry, 2nd ed., J. Goodman and J. O'Rourke, eds., CRC Press, Boca Raton, FL, 2004, pp. 743-764.
    • (2004) Handbook of Discrete and Computational Geometry , pp. 743-764
    • Mishra, B.1
  • 164
    • 0031285908 scopus 로고    scopus 로고
    • Global continuation for distance geometry problems
    • J. Moré and Z. Wu, Global continuation for distance geometry problems, SIAM J. Optim., 7 (1997), pp. 814-836.
    • (1997) SIAM J. Optim. , vol.7 , pp. 814-836
    • Moré, J.1    Wu, Z.2
  • 165
    • 0000935435 scopus 로고    scopus 로고
    • Distance geometry optimization for protein structures
    • J. Moré and Z. Wu, Distance geometry optimization for protein structures, J. Global Optim., 15 (1999), pp. 219-234.
    • (1999) J. Global Optim. , vol.15 , pp. 219-234
    • Moré, J.1    Wu, Z.2
  • 166
    • 78149241977 scopus 로고    scopus 로고
    • The branch and prune algorithm for the molecular distance geometry problem with inexact distances
    • World Academy of Science, Engineering and Technology
    • A. Mucherino and C. Lavor, The branch and prune algorithm for the molecular distance geometry problem with inexact distances, in Proceedings of the International Conference on Computational Biology, Vol. 58, World Academy of Science, Engineering and Technology, 2009, pp. 349-353.
    • (2009) Proceedings of the International Conference on Computational Biology , vol.58 , pp. 349-353
    • Mucherino, A.1    Lavor, C.2
  • 168
    • 84867418781 scopus 로고    scopus 로고
    • The discretizable distance geometry problem
    • A. Mucherino, C. Lavor, and L. Liberti, The discretizable distance geometry problem, Optim. Lett., 6 (2012), pp. 1671-1686.
    • (2012) Optim. Lett. , vol.6 , pp. 1671-1686
    • Mucherino, A.1    Lavor, C.2    Liberti, L.3
  • 169
    • 84862505760 scopus 로고    scopus 로고
    • Exploiting symmetry properties of the discretizable molecular distance geometry problem
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, On the definition of artificial backbones for the discretizable molecular distance geometry problem, Math. Balkanica (N.S.), 23 (2009), pp. 289-302.
    • (2012) J. Bioinform. Comput. Biol. , vol.10 , pp. 289-302
    • Mucherino, A.1    Lavor, C.2    Liberti, L.3
  • 170
    • 79952034699 scopus 로고    scopus 로고
    • Strategies for solving distance geometry problems with inexact distances by discrete approaches
    • S. Cafieri, E. Hendrix, L. Liberti, and F. Messine, eds., Toulouse
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, Strategies for solving distance geometry problems with inexact distances by discrete approaches, in Proceedings of the Toulouse Global Optimization Workshop, S. Cafieri, E. Hendrix, L. Liberti, and F. Messine, eds., Toulouse, 2010, pp. 93-96.
    • (2010) Proceedings of the Toulouse Global Optimization Workshop , pp. 93-96
    • Mucherino, A.1    Lavor, C.2    Liberti, L.3    Maculan, N.4
  • 174
    • 79956223394 scopus 로고    scopus 로고
    • The molecular distance geometry problem applied to protein conformations
    • S. Cafieri, A. Mucherino, G. Nannicini, F. Tarissan, and L. Liberti, eds., École Polytechnique, Paris
    • A. Mucherino, C. Lavor, and N. Maculan, The molecular distance geometry problem applied to protein conformations, in Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, S. Cafieri, A. Mucherino, G. Nannicini, F. Tarissan, and L. Liberti, eds., École Polytechnique, Paris, 2009, pp. 337-340.
    • (2009) Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization , pp. 337-340
    • Mucherino, A.1    Lavor, C.2    Maculan, N.3
  • 175
    • 79955851810 scopus 로고    scopus 로고
    • Influence of pruning devices on the solution of molecular distance geometry problems
    • P. Pardalos and S. Rebennack, eds., Lecture Notes in Comput. Sci. 6630, Springer, Berlin
    • A. Mucherino, C. Lavor, T. Malliavin, L. Liberti, M. Nilges, and N. Maculan, Influence of pruning devices on the solution of molecular distance geometry problems, in Experimental Algorithms, P. Pardalos and S. Rebennack, eds., Lecture Notes in Comput. Sci. 6630, Springer, Berlin, 2011, pp. 206-217.
    • (2011) Experimental Algorithms , pp. 206-217
    • Mucherino, A.1    Lavor, C.2    Malliavin, T.3    Liberti, L.4    Nilges, M.5    Maculan, N.6
  • 176
    • 78149236724 scopus 로고    scopus 로고
    • MD-jeep: An implementation of a branch-andprune algorithm for distance geometry problems
    • K. Fukuda, J. van der Hoeven, M. Joswig, and N. Takayama, eds., Lecture Notes in Comput. Sci. 6327, Springer, New York
    • A. Mucherino, L. Liberti, and C. Lavor, MD-jeep: An implementation of a branch-andprune algorithm for distance geometry problems, in Mathematical Software, K. Fukuda, J. van der Hoeven, M. Joswig, and N. Takayama, eds., Lecture Notes in Comput. Sci. 6327, Springer, New York, 2010, pp. 186-197.
    • (2010) Mathematical Software , pp. 186-197
    • Mucherino, A.1    Liberti, L.2    Lavor, C.3
  • 177
    • 72749092411 scopus 로고    scopus 로고
    • Comparisons between an exact and a metaheuristic algorithm for the molecular distance geometry problem
    • F. Rothlauf, ed., Montreal, ACM, New York
    • A. Mucherino, L. Liberti, C. Lavor, and N. Maculan, Comparisons between an exact and a metaheuristic algorithm for the molecular distance geometry problem, in Proceedings of the Genetic and Evolutionary Computation Conference, F. Rothlauf, ed., Montreal, ACM, New York, 2009, pp. 333-340.
    • (2009) Proceedings of the Genetic and Evolutionary Computation Conference , pp. 333-340
    • Mucherino, A.1    Liberti, L.2    Lavor, C.3    Maculan, N.4
  • 178
    • 0033322289 scopus 로고    scopus 로고
    • On the kinematic analysis of robotic mechanisms
    • J. Nielsen and B. Roth, On the kinematic analysis of robotic mechanisms, Internat. J. Robotics Res., 18 (1999), pp. 1147-1160.
    • (1999) Internat. J. Robotics Res. , vol.18 , pp. 1147-1160
    • Nielsen, J.1    Roth, B.2
  • 179
    • 0031566434 scopus 로고    scopus 로고
    • Automated NOESY interpretation with ambiguous distance restraints: The refined NMR solution structure of the Pleckstrin homology domain from β-spectrin
    • M. Nilges, M. Macias, S. O'Donoghue, and H. Oschkinat, Automated NOESY interpretation with ambiguous distance restraints: The refined NMR solution structure of the Pleckstrin homology domain from β-spectrin, J. Molecular Biol., 269 (1997), pp. 408-422.
    • (1997) J. Molecular Biol. , vol.269 , pp. 408-422
    • Nilges, M.1    Macias, M.2    O'Donoghue, S.3    Oschkinat, H.4
  • 180
    • 84893842842 scopus 로고    scopus 로고
    • Solving the discretizable molecular distance geometry problem by multiple realization trees
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York
    • P. Nucci, L. Nogueira, and C. Lavor, Solving the discretizable molecular distance geometry problem by multiple realization trees, in Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York, 2013, pp. 161-176.
    • (2013) Distance Geometry: Theory, Methods, and Applications , pp. 161-176
    • Nucci, P.1    Nogueira, L.2    Lavor, C.3
  • 181
    • 84893853274 scopus 로고    scopus 로고
    • Sphere unions and intersections and some of their applications in molecular modeling
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York
    • M. Petitjean, Sphere unions and intersections and some of their applications in molecular modeling, in Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York, 2013, pp. 61-83.
    • (2013) Distance Geometry: Theory, Methods, and Applications , pp. 61-83
    • Petitjean, M.1
  • 182
    • 81255163192 scopus 로고    scopus 로고
    • (Robust) edge-based semidefinite programming relaxation of sensor network localization
    • T. Pong and P. Tseng, (Robust) edge-based semidefinite programming relaxation of sensor network localization, Math. Program. Ser. A, 130 (2011), pp. 321-358.
    • (2011) Math. Program. Ser. A , vol.130 , pp. 321-358
    • Pong, T.1    Tseng, P.2
  • 184
    • 18144405777 scopus 로고    scopus 로고
    • A branch-and-prune solver for distance constraints
    • J. Porta, L. Ros, F. Thomas, and C. Torras, A branch-and-prune solver for distance constraints, IEEE Trans. Robotics, 21 (2005), pp. 176-187.
    • (2005) IEEE Trans. Robotics , vol.21 , pp. 176-187
    • Porta, J.1    Ros, L.2    Thomas, F.3    Torras, C.4
  • 185
    • 0032012684 scopus 로고    scopus 로고
    • Inverse kinematic solution of robot manipulators using interval analysis
    • R. Rao, A. Asaithambi, and S. Agrawal, Inverse kinematic solution of robot manipulators using interval analysis, ASME J. Mech. Design, 120 (1998), pp. 147-150.
    • (1998) ASME J. Mech. Design , vol.120 , pp. 147-150
    • Rao, R.1    Asaithambi, A.2    Agrawal, S.3
  • 186
  • 187
    • 0021409159 scopus 로고
    • A network theory approach to the rigidity of skeletal structures. Part 2. Laman's theorem and topological formulae
    • A. Recski, A network theory approach to the rigidity of skeletal structures. Part 2. Laman's theorem and topological formulae, Discrete Appl. Math., 8 (1984), pp. 63-68.
    • (1984) Discrete Appl. Math. , vol.8 , pp. 63-68
    • Recski, A.1
  • 189
    • 0001580189 scopus 로고
    • Algorithmic aspects of vertex elimination on graphs
    • D. J. Rose, R. E. Tarjan, and G. S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5 (1976), pp. 266-283.
    • (1976) SIAM J. Comput. , vol.5 , pp. 266-283
    • Rose, D.J.1    Tarjan, R.E.2    Lueker, G.S.3
  • 190
    • 0003167703 scopus 로고
    • Rigid and flexible frameworks
    • B. Roth, Rigid and flexible frameworks, Amer. Math. Monthly, 88 (1981), pp. 6-21.
    • (1981) Amer. Math. Monthly , vol.88 , pp. 6-21
    • Roth, B.1
  • 191
    • 85025197290 scopus 로고
    • Synthesis of path-generating mechanisms by numerical methods
    • B. Roth and F. Freudenstein, Synthesis of path-generating mechanisms by numerical methods, J. Engrg. Industry, 85 (1963), pp. 298-307.
    • (1963) J. Engrg. Industry , vol.85 , pp. 298-307
    • Roth, B.1    Freudenstein, F.2
  • 193
    • 33845462136 scopus 로고    scopus 로고
    • Side chain placement using estimation of distribution algorithms
    • R. Santana, P. Larrañaga, and J. Lozano, Side chain placement using estimation of distribution algorithms, Art. Intell. Med., 39 (2007), pp. 49-63.
    • (2007) Art. Intell. Med. , vol.39 , pp. 49-63
    • Santana, R.1    Larrañaga, P.2    Lozano, J.3
  • 199
    • 0001203499 scopus 로고
    • Remarks to Maurice Fréchet's article "sur la définition axiomatique d'une classe d'espaces distanciés vectoriellement applicable sur l'espace de Hilbert"
    • I. Schoenberg, Remarks to Maurice Fréchet's article "Sur la définition axiomatique d'une classe d'espaces distanciés vectoriellement applicable sur l'espace de Hilbert," Ann. of Math., 36 (1935), pp. 724-732.
    • (1935) Ann. of Math. , vol.36 , pp. 724-732
    • Schoenberg, I.1
  • 200
    • 33645388684 scopus 로고    scopus 로고
    • Generic and abstract rigidity
    • M. Thorpe and P. Duxbury, eds., Fundamental Materials Research, Springer, New York
    • B. Servatius and H. Servatius, Generic and abstract rigidity, in Rigidity Theory and Applications, M. Thorpe and P. Duxbury, eds., Fundamental Materials Research, Springer, New York, 2002, pp. 1-19.
    • (2002) Rigidity Theory and Applications , pp. 1-19
    • Servatius, B.1    Servatius, H.2
  • 201
    • 34250926052 scopus 로고
    • The analysis of proximities: Multidimensional scaling with an unknown distance function, Part i
    • R. Shepard, The analysis of proximities: Multidimensional scaling with an unknown distance function, Part I, Psychometrika, 27 (1962), pp. 125-140.
    • (1962) Psychometrika , vol.27 , pp. 125-140
    • Shepard, R.1
  • 202
    • 34250920725 scopus 로고
    • The analysis of proximities: Multidimensional scaling with an unknown distance function, Part II
    • R. Shepard, The analysis of proximities: Multidimensional scaling with an unknown distance function, Part II, Psychometrika, 27 (1962), pp. 219-246.
    • (1962) Psychometrika , vol.27 , pp. 219-246
    • Shepard, R.1
  • 203
    • 0000303959 scopus 로고
    • Metric structures in ordinal data
    • R. Shepard, Metric structures in ordinal data, J. Math. Psych., 3 (1966), pp. 287-315.
    • (1966) J. Math. Psych. , vol.3 , pp. 287-315
    • Shepard, R.1
  • 204
    • 78649320169 scopus 로고    scopus 로고
    • Angular synchronization by eigenvectors and semidefinite programming
    • A. Singer, Angular synchronization by eigenvectors and semidefinite programming, Appl. Comput. Harmon. Anal., 30 (2011), pp. 20-36.
    • (2011) Appl. Comput. Harmon. Anal. , vol.30 , pp. 20-36
    • Singer, A.1
  • 205
    • 77956028031 scopus 로고    scopus 로고
    • Uniqueness of low-rank matrix completion by rigidity theory
    • A. Singer and M. Cucuringu, Uniqueness of low-rank matrix completion by rigidity theory, SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1621-1641.
    • (2010) SIAM J. Matrix Anal. Appl. , vol.31 , pp. 1621-1641
    • Singer, A.1    Cucuringu, M.2
  • 206
    • 80051753409 scopus 로고    scopus 로고
    • Viewing angle classification of cryoelectron microscopy images using eigenvectors
    • A. Singer, Z. Zhao, Y. Shkolnisky, and R. Hadani, Viewing angle classification of cryoelectron microscopy images using eigenvectors, SIAM J. Imaging Sci., 4 (2011), pp. 723-759.
    • (2011) SIAM J. Imaging Sci. , vol.4 , pp. 723-759
    • Singer, A.1    Zhao, Z.2    Shkolnisky, Y.3    Hadani, R.4
  • 207
    • 0022048703 scopus 로고
    • Solution of the embedding problem and decomposition of symmetric matrices
    • M. Sippl and H. Scheraga, Solution of the embedding problem and decomposition of symmetric matrices, Proc. Natl. Acad. Sci. USA, 82 (1985), pp. 2197-2201.
    • (1985) Proc. Natl. Acad. Sci. USA , vol.82 , pp. 2197-2201
    • Sippl, M.1    Scheraga, H.2
  • 210
    • 84887163959 scopus 로고    scopus 로고
    • Solving the molecular distance geometry problem with inaccurate distance data
    • M. Souza, C. Lavor, A. Muritiba, and N. Maculan, Solving the molecular distance geometry problem with inaccurate distance data, BMC Bioinform., 14 (2013), pp. S71-S76.
    • (2013) BMC Bioinform. , vol.14
    • Souza, M.1    Lavor, C.2    Muritiba, A.3    Maculan, N.4
  • 211
    • 80855147528 scopus 로고    scopus 로고
    • Hyperbolic smoothing and penalty techniques applied to molecular structure determination
    • M. Souza, A. Xavier, C. Lavor, and N. Maculan, Hyperbolic smoothing and penalty techniques applied to molecular structure determination, Oper. Res. Lett., 39 (2011), pp. 461-465.
    • (2011) Oper. Res. Lett. , vol.39 , pp. 461-465
    • Souza, M.1    Xavier, A.2    Lavor, C.3    Maculan, N.4
  • 212
  • 213
    • 84893877591 scopus 로고
    • Hirzel, Leipzig
    • C. Stumpf, Tonpsychologie, Vol. II, Hirzel, Leipzig, 1890.
    • (1890) Tonpsychologie , vol.2
    • Stumpf, C.1
  • 214
    • 37549072578 scopus 로고
    • Chemistry and algebra
    • J. Sylvester, Chemistry and algebra, Nature, 17 (1877), pp. 284-284.
    • (1877) Nature , vol.17 , pp. 284-284
    • Sylvester, J.1
  • 215
    • 34250297158 scopus 로고
    • Nonmetric individual differences in multidimensional scaling: An alternating least squares method with optimal scaling features
    • Y. Takane, F. Young, and J. De Leeuw, Nonmetric individual differences in multidimensional scaling: An alternating least squares method with optimal scaling features, Psychometrika, 42 (1977), pp. 7-67.
    • (1977) Psychometrika , vol.42 , pp. 7-67
    • Takane, Y.1    Young, F.2    De Leeuw, J.3
  • 216
    • 0033164017 scopus 로고    scopus 로고
    • On the generic rigidity of bar-frameworks
    • T.-S. Tay, On the generic rigidity of bar-frameworks, Adv. Appl. Math., 23 (1999), pp. 14-28.
    • (1999) Adv. Appl. Math. , vol.23 , pp. 14-28
    • Tay, T.-S.1
  • 217
    • 0001963291 scopus 로고
    • Generating isostatic frameworks
    • T.-S. Tay and W. Whiteley, Generating isostatic frameworks, Struct. Topology, 11 (1985), pp. 21-69.
    • (1985) Struct. Topology , vol.11 , pp. 21-69
    • Tay, T.-S.1    Whiteley, W.2
  • 218
    • 0034704229 scopus 로고    scopus 로고
    • A global geometric framework for nonlinear dimensionality reduction
    • J. Tenenbaum, V. de Silva, and J. Langford, A global geometric framework for nonlinear dimensionality reduction, Science, 290 (2000), pp. 2319-2322.
    • (2000) Science , vol.290 , pp. 2319-2322
    • Tenenbaum, J.1    De Silva, V.2    Langford, J.3
  • 219
    • 33846144346 scopus 로고    scopus 로고
    • Distance constraints solved geometrically
    • G. Galletti and J. Lenarcic, eds., Kluwer, Dordrecht
    • F. Thomas, J. Porta, and L. Ros, Distance constraints solved geometrically, in Advances in Robot Kinematics, G. Galletti and J. Lenarcic, eds., Kluwer, Dordrecht, 2004, pp. 123-132.
    • (2004) Advances in Robot Kinematics , pp. 123-132
    • Thomas, F.1    Porta, J.2    Ros, L.3
  • 220
    • 38249026284 scopus 로고
    • The graph genus problem is NP-complete
    • C. Thomassen, The graph genus problem is NP-complete, J. Algorithms, 10 (1989), pp. 568-576.
    • (1989) J. Algorithms , vol.10 , pp. 568-576
    • Thomassen, C.1
  • 221
    • 0034257838 scopus 로고    scopus 로고
    • Real-time inverse kinematics techniques for anthropomorphic limbs
    • D. Tolani, A. Goswami, and N. Badler, Real-time inverse kinematics techniques for anthropomorphic limbs, Graphical Models, 62 (2000), pp. 353-388.
    • (2000) Graphical Models , vol.62 , pp. 353-388
    • Tolani, D.1    Goswami, A.2    Badler, N.3
  • 223
    • 0022075423 scopus 로고
    • Solving the kinematics of the most general six-and five-degree-offreedom manipulators by continuation methods
    • L. Tsai and A. Morgan, Solving the kinematics of the most general six-and five-degree-offreedom manipulators by continuation methods, J. Mech. Transmissions Automation in Design, 107 (1985), pp. 189-200.
    • (1985) J. Mech. Transmissions Automation in Design , vol.107 , pp. 189-200
    • Tsai, L.1    Morgan, A.2
  • 224
    • 0035533631 scopus 로고    scopus 로고
    • Convergence of a block coordinate descent method for nondifferentiable minimization
    • P. Tseng, Convergence of a block coordinate descent method for nondifferentiable minimization, J. Optim. Theory Appl., 109 (2001), pp. 475-494.
    • (2001) J. Optim. Theory Appl. , vol.109 , pp. 475-494
    • Tseng, P.1
  • 225
    • 39449085876 scopus 로고    scopus 로고
    • Second-order cone programming relaxations of sensor network localization
    • P. Tseng, Second-order cone programming relaxations of sensor network localization, SIAM J. Optim., 18 (2007), pp. 156-185.
    • (2007) SIAM J. Optim. , vol.18 , pp. 156-185
    • Tseng, P.1
  • 227
    • 84893845439 scopus 로고    scopus 로고
    • Distance geometry methods for protein structure determination
    • A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York
    • Z. Voller and Z. Wu, Distance geometry methods for protein structure determination, in Distance Geometry: Theory, Methods, and Applications, A. Mucherino, C. Lavor, L. Liberti, and N. Maculan, eds., Springer, New York, 2013, pp. 139-159.
    • (2013) Distance Geometry: Theory, Methods, and Applications , pp. 139-159
    • Voller, Z.1    Wu, Z.2
  • 229
    • 84988473168 scopus 로고
    • Numerical continuation methods for solving polynomial systems arising in kinematics
    • C. Wampler, A. Morgan, and A. Sommese, Numerical continuation methods for solving polynomial systems arising in kinematics, J. Mech. Design, 112 (1990), pp. 59-68.
    • (1990) J. Mech. Design , vol.112 , pp. 59-68
    • Wampler, C.1    Morgan, A.2    Sommese, A.3
  • 230
    • 60549085200 scopus 로고    scopus 로고
    • Further relaxations of the semidefinite programming approach to sensor network localization
    • Z. Wang, S. Zheng, Y. Ye, and S. Boyd, Further relaxations of the semidefinite programming approach to sensor network localization, SIAM J. Optim., 19 (2008), pp. 655-673.
    • (2008) SIAM J. Optim. , vol.19 , pp. 655-673
    • Wang, Z.1    Zheng, S.2    Ye, Y.3    Boyd, S.4
  • 231
    • 84976653144 scopus 로고
    • Some computer science issues in ubiquitous computing
    • M. Weiser, Some computer science issues in ubiquitous computing, Comm. ACM, 36 (1993), pp. 75-84.
    • (1993) Comm. ACM , vol.36 , pp. 75-84
    • Weiser, M.1
  • 232
    • 84968494918 scopus 로고
    • Infinitesimally rigid polyhedra. I. Statics of frameworks
    • W. Whiteley, Infinitesimally rigid polyhedra. I. Statics of frameworks, Trans. Amer. Math. Soc., 285 (1984), pp. 431-465.
    • (1984) Trans. Amer. Math. Soc. , vol.285 , pp. 431-465
    • Whiteley, W.1
  • 233
    • 8744294682 scopus 로고    scopus 로고
    • Rigidity and scene analysis
    • J. Goodman and J. O'Rourke, eds., CRC Press, Boca Raton, FL
    • W. Whiteley, Rigidity and scene analysis, in Handbook of Discrete and Computational Geometry, J. Goodman and J. O'Rourke, eds., CRC Press, Boca Raton, FL, 2004.
    • (2004) Handbook of Discrete and Computational Geometry
    • Whiteley, W.1
  • 234
    • 0035156982 scopus 로고    scopus 로고
    • Constrained global optimization for estimating molecular structure from atomic distances
    • G. Williams, J. Dugan, and R. Altman, Constrained global optimization for estimating molecular structure from atomic distances, J. Comput. Biol., 8 (2001), pp. 523-547.
    • (2001) J. Comput. Biol. , vol.8 , pp. 523-547
    • Williams, G.1    Dugan, J.2    Altman, R.3
  • 235
    • 33847251002 scopus 로고    scopus 로고
    • An updated geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data
    • D. Wu and Z. Wu, An updated geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data, J. Global Optim., 37 (2007), pp. 661-673.
    • (2007) J. Global Optim. , vol.37 , pp. 661-673
    • Wu, D.1    Wu, Z.2
  • 236
    • 43249103721 scopus 로고    scopus 로고
    • Rigid versus unique determination of protein structures with geometric buildup
    • D. Wu, Z. Wu, and Y. Yuan, Rigid versus unique determination of protein structures with geometric buildup, Optim. Lett., 2 (2008), pp. 319-331.
    • (2008) Optim. Lett. , vol.2 , pp. 319-331
    • Wu, D.1    Wu, Z.2    Yuan, Y.3
  • 237
    • 0024587230 scopus 로고
    • Protein structure determination in solution by nuclear magnetic resonance spectroscopy
    • K. Wüthrich, Protein structure determination in solution by nuclear magnetic resonance spectroscopy, Science, 243 (1989), pp. 45-50.
    • (1989) Science , vol.243 , pp. 45-50
    • Wü Thrich, K.1
  • 238
    • 0021095743 scopus 로고
    • Pseudo-structures for the 20 common amino acids for use in studies of protein conformations by measurements of intramolecular proton-proton distance constraints with nuclear magnetic resonance
    • K. Wüthrich, M. Billeter, and W. Braun, Pseudo-structures for the 20 common amino acids for use in studies of protein conformations by measurements of intramolecular proton-proton distance constraints with nuclear magnetic resonance, J. Molecular Biol., 169 (1983), pp. 949-961.
    • (1983) J. Molecular Biol. , vol.169 , pp. 949-961
    • Wüthrich, K.1    Billeter, M.2    Braun, W.3
  • 240
    • 33750706214 scopus 로고    scopus 로고
    • Solving spatial constraints with global distance coordinate system
    • L. Yang, Solving spatial constraints with global distance coordinate system, J. Comput. Geom. Appl., 16 (2006), pp. 533-547.
    • (2006) J. Comput. Geom. Appl. , vol.16 , pp. 533-547
    • Yang, L.1
  • 241
    • 84893867487 scopus 로고
    • The positioning problem-A draft of an intermediate summary
    • Carnegie-Mellon University, Pittsburgh
    • Y. Yemini, The positioning problem-a draft of an intermediate summary, in Proceedings of the Conference on Distributed Sensor Networks, Carnegie-Mellon University, Pittsburgh, 1978, pp. 137-145.
    • (1978) Proceedings of the Conference on Distributed Sensor Networks , pp. 137-145
    • Yemini, Y.1
  • 244
    • 79251528892 scopus 로고    scopus 로고
    • Universal rigidity and edge sparsification for sensor network localization
    • Z. Zhu, A. Man-Cho So, and Y. Ye, Universal rigidity and edge sparsification for sensor network localization, SIAM J. Optim., 20 (2010), pp. 3059-3081.
    • (2010) SIAM J. Optim. , vol.20 , pp. 3059-3081
    • Zhu, Z.1    Man-Cho So, A.2    Ye, Y.3
  • 245
    • 59449108414 scopus 로고    scopus 로고
    • Branch and bound algorithm for multidimensional scaling with city-block metric
    • A. Žilinskas and J. Žilinskas, Branch and bound algorithm for multidimensional scaling with city-block metric, J. Global Optim., 43 (2009), pp. 357-372.
    • (2009) J. Global Optim. , vol.43 , pp. 357-372
    • Žilinskas, A.1    Žilinskas, J.2


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