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Linked References

1. P. Biswas and Y. Ye, “Semidefinite programming for ad hoc wireless sensor network localization,” in Proceedings of the Third International Symposium on Information Processing in Sensor Networks, (IPSN '04), pp. 46–54, New York, NY, USA, April 2004.
2. M. W. Carter, H. H. Jin, M. A. Saunders, and Y. Ye, “SpaseLoc: an adaptive subproblem algorithm for scalable wireless sensor network localization,” SIAM Journal on Optimization, vol. 17, no. 4, pp. 1102–1128, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
3. D. Culler and W. Hong, “Wireless sensor networks,” Communications of the ACM, vol. 47, pp. 30–33, 2004.
4. T.-H. Yi, H.-N. Li, and M. Gu, “Optimal sensor placement for health monitoring of high-rise structure based on genetic algorithm,” Mathematical Problems in Engineering, vol. 2011, Article ID 395101, 12 pages, 2011.
5. T. Gao, D. Greenspan, M. Welsh, R. R. Juang, and A. Alm, “Vital signs monitoring and patient tracking over a wireless network,” in Proceedings of the 27th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, (EMBS '05), pp. 102–105, Shanghai, China, September 2005.
6. M. Lawlor, “Small systems, big business,” Signal Magazine, 2005.
7. A. Dragoon, “Small wonders,” CIO Magazine, 2005.
8. J. B. Saxe, “Embeddability of weighted graphs in k-space is strongly NP-hard,” in Proceedings of the 17th Allerton Conference in Communication, Control and Computing, pp. 480–489, Monticello, Ill, USA, 1979.
9. G. M. Crippen and T. F. Havel, Distance Geometry and Molecular Conformation, Research Studies Press, Chichester, UK, 1988.
10. J. J. More and Z. Wu, “ε-optimal solutions to distance geometry problems via global continuation,” in Global Minimization of Non-Convex Energy Functions, P. M. Pardalos, D. Shalloway, and G. Xue, Eds., pp. 151–168, American Mathematical Society, Providence, RI, USA, 1996.
11. Q. Dong and Z. Wu, “A linear-time algorithm for solving the molecular distance geometry problem with exact inter-atomic distances,” Journal of Global Optimization, vol. 22, no. 1-4, pp. 365–375, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
12. P. Biswas, T.-C. Lian, T.-C. Wang, and Y. Ye, “Semidefinite programming based algorithms for sensor network localization,” ACM Transactions on Sensor Networks, vol. 2, no. 2, pp. 188–220, 2006. View at Publisher · View at Google Scholar
13. Z. Wang, S. Zheng, Y. Ye, and S. Boyd, “Further relaxations of the semidefinite programming approach to sensor network localization,” SIAM Journal on Optimization, vol. 19, no. 2, pp. 655–673, 2008. View at Publisher · View at Google Scholar
14. J. Nie, “Sum of squares method for sensor network localization,” Computational Optimization and Applications, vol. 43, no. 2, pp. 151–179, 2009. View at Publisher · View at Google Scholar
15. P. Tseng, “Second-order cone programming relaxation of sensor network localization,” SIAM Journal on Optimization, vol. 18, no. 1, pp. 156–185, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
16. S. Kim, M. Kojima, and H. Waki, “Exploiting sparsity in SDP relaxation for sensor network localization,” SIAM Journal on Optimization, vol. 20, no. 1, pp. 192–215, 2009. View at Publisher · View at Google Scholar
17. Z. Zhu, A. M.-C. So, and Y. Ye, “Universal rigidity and edge sparsification for sensor network localization,” SIAM Journal on Optimization, vol. 20, no. 6, pp. 3059–3081, 2010. View at Publisher · View at Google Scholar
18. T. K. Pong and P. Tseng, “(Robust) edge-based semidefinite programming relaxation of sensor network localization,” Mathematical Programming. In press. View at Publisher · View at Google Scholar
19. N. Krislock and H. Wolkowicz, “Explicit sensor network localization using semidefinite representations and facial reductions,” SIAM Journal on Optimization, vol. 20, no. 5, pp. 2679–2708, 2010. View at Publisher · View at Google Scholar
20. N. Krislock, Semidefinite facial reduction for low-rank euclidean distance matrix completion, Ph.D. thesis, University of Waterloo, Waterloo, Canada, 2010.
21. Q. Dong and Z. Wu, “A geometric build-up algorithm for solving the molecular distance geometry problem with sparse distance data,” Journal of Global Optimization, vol. 26, no. 3, pp. 321–333, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
22. D. Wu and Z. Wu, “An updated geometric build-up algorithm for solving the molecular distance geometry problems with sparse distance data,” Journal of Global Optimization, vol. 37, no. 4, pp. 661–673, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
23. D. Wu, Z. Wu, and Y. Yuan, “Rigid versus unique determination of protein structures with geometric buildup,” Optimization Letters, vol. 2, no. 3, pp. 319–331, 2008. View at Publisher · View at Google Scholar
24. A. Sit, Z. Wu, and Y. Yuan, “A geometric buildup algorithm for the solution of the distance geometry problem using least-squares approximation,” Bulletin of Mathematical Biology, vol. 71, no. 8, pp. 1914–1933, 2009. View at Publisher · View at Google Scholar · View at PubMed
25. A. Sit and Z. Wu, “Solving a generalized distance geometry problem for protein structure determination,” Bulletin of Mathematical Biology. In press. View at Publisher · View at Google Scholar · View at PubMed
26. C. Eckart and G. Young, “The approximation of one matrix by another of lower rank,” Psychometrika, vol. 1, no. 3, pp. 211–218, 1936. View at Publisher · View at Google Scholar
27. R. Mathar and R. Meyer, “Preorderings, monotone functions, and best rank r approximations with applications to classical MDS,” Journal of Statistical Planning and Inference, vol. 37, no. 3, pp. 291–305, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
28. T. F. Cox and M. A. A. Cox, Multidimensional Scaling, Chapman and Hall, London, UK, 2en edition, 1994.
29. W. S. Torgerson, “Multidimensional scaling. I. Theory and method,” Psychometrika, vol. 17, pp. 401–419, 1952.
30. G. H. Golub and C. F. V. Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, Md, USA, 1989.
31. R. M. Karp, “Reducibility among combinatorial problems,” in Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, Eds., pp. 85–103, Plenum Press, New York, NY, USA, 1972.
32. J. M. Robson, “Finding a maximum independent set in time O(2^n/4),” Technical Report 1251-01, Université Bordeaux I, Bordeaux, France, 2001.