\def\cprime{$'$} \def\cprime{$'$} \def\cprime{$'$}
  \def\udot#1{\ifmmode\oalign{$#1$\crcr\hidewidth.\hidewidth
  }\else\oalign{#1\crcr\hidewidth.\hidewidth}\fi} \def\cprime{$'$}
  \def\cprime{$'$} \def\cprime{$'$}
\begin{thebibliography}{10}

\bibitem{homwolkA:04}
S.~Al-Homidan and H.~Wolkowicz.
\newblock Approximate and exact completion problems for {E}uclidean distance
  matrices using semidefinite programming.
\newblock {\em Linear Algebra Appl.}, 406:109--141, 2005.

\bibitem{AlKaWo:97}
A.~Alfakih, A.~Khandani, and H.~Wolkowicz.
\newblock Solving {E}uclidean distance matrix completion problems via
  semidefinite programming.
\newblock {\em Comput. Optim. Appl.}, 12(1-3):13--30, 1999.
\newblock A tribute to Olvi Mangasarian.

\bibitem{MR1758031}
L.T.H. AN and P.D. TAO.
\newblock Large scale molecular conformation via the exact distance geometry
  problem.
\newblock In {\em Optimization ({N}amur, 1998)}, volume 481 of {\em Lecture
  Notes in Econom. and Math. Systems}, pages 260--277. Springer, Berlin, 2000.

\bibitem{BYIEEE:06}
P.~Biswas, T.-C. Liang, K.-C. Toh, , Y.~Ye, and T.-C. Wang.
\newblock Semidefinite programming approaches for sensor network localization
  with noisy distance measurements.
\newblock {\em IEEE Transactions on Automation Science and Engineering},
  3:360--371, 2006.

\bibitem{MR2274505}
M.W. Carter, H.H. Jin, M.A. Saunders, and Y.~Ye.
\newblock Spase{L}oc: an adaptive subproblem algorithm for scalable wireless
  sensor network localization.
\newblock {\em SIAM J. Optim.}, 17(4):1102--1128, 2006.

\bibitem{MR1282736}
A.R. Conn, N.~Gould, M.~LESCRENIER, and P.L. Toint.
\newblock Performance of a multifrontal scheme for partially separable
  optimization.
\newblock In {\em Advances in optimization and numerical analysis (Oaxaca,
  1992)}, volume 275 of {\em Math. Appl.}, pages 79--96. Kluwer Acad. Publ.,
  Dordrecht, 1994.

\bibitem{MR1307166}
A.R. Conn, N.~Gould, and P.L. Toint.
\newblock Improving the decomposition of partially separable functions in the
  context of large-scale optimization: a first approach.
\newblock In {\em Large scale optimization (Gainesville, FL, 1993)}, pages
  82--94. Kluwer Acad. Publ., Dordrecht, 1994.

\bibitem{MR1480634}
M.J. DAYD{\'E}, J.Y. L'EXCELLENT, and N.I.M. Gould.
\newblock Element-by-element preconditioners for large partially separable
  optimization problems.
\newblock {\em SIAM J. Sci. Comput.}, 18(6):1767--1787, 1997.

\bibitem{DiKrQiWo:08}
Y.~Ding, N.~Krislock, J.~Qian, and H.~Wolkowicz.
\newblock Sensor network localization, {E}uclidean distance matrix completions,
  and graph realization.
\newblock In {\em Proceedings of the First ACM International Workshop on Mobile
  Entity Localization and Tracking in GPS-Less Environment, San Francisco},
  pages 129--134, 2008.

\bibitem{DiKrQiWo:06}
Y.~Ding, N.~Krislock, J.~Qian, and H.~Wolkowicz.
\newblock Sensor network localization, {E}uclidean distance matrix completions,
  and graph realization.
\newblock {\em Optim. Eng.}, 11(1):45--66, 2010.

\bibitem{MR1878150}
Q.~Dong and Z.~Wu.
\newblock A linear-time algorithm for solving the molecular distance geometry
  problem with exact inter-atomic distances.
\newblock {\em J. Global Optim.}, 22(1-4):365--375, 2002.
\newblock Dedicated to Professor Reiner Horst on his 60th birthday.

\bibitem{MR1977953}
Q.~Dong and Z.~Wu.
\newblock A geometric build-up algorithm for solving the molecular distance
  geometry problem with sparse distance data.
\newblock {\em J. Global Optim.}, 26(3):321--333, 2003.

\bibitem{MR2457932}
R.~DOS SANTOS~CARVALHO, C.~LAVOR, and F.~PROTTI.
\newblock Extending the geometric build-up algorithm for the molecular distance
  geometry problem.
\newblock {\em Inform. Process. Lett.}, 108(4):234--237, 2008.

\bibitem{Fan:49}
K.~Fan.
\newblock On a theorem of weyl concerning eigenvalues of linear transformations
  i.
\newblock {\em Proc.\ Nat.\ Acad.\ Sci.\ U.S.A.}, 35:652--655, 1949.

\bibitem{MR760465}
A.~GRIEWANK and P.L. Toint.
\newblock Numerical experiments with partially separable optimization problems.
\newblock In {\em Numerical analysis (Dundee, 1983)}, volume 1066 of {\em
  Lecture Notes in Math.}, pages 203--220. Springer, Berlin, 1984.

\bibitem{GrTo:82c}
A.O. GRIEWANK and P.L. Toint.
\newblock On the unconstrained optimization of partially separable functions.
\newblock In M.J.D. Powell, editor, {\em Nonlinear Optimization}. Academic
  Press, London, 1982.

\bibitem{KimKojimaWaki:09}
S.~Kim, M.~Kojima, and H.~Waki.
\newblock Exploiting sparsity in {SDP} relaxation for sensor network
  localization.
\newblock {\em SIAM J. Optim.}, 20(1):192--215, 2009.

\bibitem{krislock:2010}
N.~Krislock.
\newblock {\em Semidefinite Facial Reduction for Low-Rank Euclidean Distance
  Matrix Completion}.
\newblock PhD thesis, University of Waterloo, 2010.

\bibitem{kriswolk:09}
N.~Krislock and H.~Wolkowicz.
\newblock Explicit sensor network localization using semidefinite
  representations and facial reductions.
\newblock {\em SIAM Journal on Optimization}, 20(5):2679--2708, 2010.

\bibitem{MR2206961}
C.~LAVOR.
\newblock On generating instances for the molecular distance geometry problem.
\newblock In {\em Global optimization}, volume~84 of {\em Nonconvex Optim.
  Appl.}, pages 405--414. Springer, New York, 2006.

\bibitem{MR943994}
W.W. Lin.
\newblock The computation of the {K}ronecker canonical form of an arbitrary
  symmetric pencil.
\newblock {\em Linear Algebra Appl.}, 103:41--71, 1988.

\bibitem{MarshOlk:79}
A.W. Marshall and I.~Olkin.
\newblock {\em Inequalities: Theory of Majorization and its Applications}.
\newblock Academic Press, New York, NY, 1979.

\bibitem{NieCOAP07}
J.~Nie.
\newblock Sum of squares method for sensor network localization.
\newblock {\em Comput. Optim. Appl.}, 43:151--179, 2009.

\bibitem{Savarese:01}
C.~SAVARESE, J.~RABAEY, , and J.~BEUTEL.
\newblock Locationing in distributed ad-hoc wireless sensor networks.
\newblock In {\em IEEE Int. Conf. on Acoustics, Speech, and Signal Processing
  (ICASSP)}, pages 2037--2040, 2001.

\bibitem{Savvides:01}
A.~SAVVIDES, C.C. HAN, and M.B. SRIVASTAVA.
\newblock Dynamic fine grained localization in ad-hoc sensor networks.
\newblock In {\em Proceedings of the Fifth International Conference on Mobile
  Computing and Networking (Mobicom 2001)}, pages 166--179, 2001.

\bibitem{MR866412}
P.L. Toint.
\newblock Global convergence of the partitioned {BFGS} algorithm for convex
  partially separable optimization.
\newblock {\em Math. Programming}, 36(3):290--306, 1986.

\end{thebibliography}