Mathematical Programming

, Volume 109, Issue 2–3, pp 367–384 | Cite as

Theory of semidefinite programming for Sensor Network Localization



We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance measures. Therefore, we show, for the first time, that these networks can be localized in polynomial time. We also give a simple and efficient criterion for checking whether a given instance of the localization problem has a unique realization in \(\mathcal{R}^2\) using graph rigidity theory. Finally, we introduce a notion called strong localizability and show that the SDP model will identify all strongly localizable sub-networks in the input network.


Euclidean distance geometry Graph realization Sensor network localization Semidefinite programming Rigidity theory 

Mathematics Subject Classification (2000)

51K05 52C25 68Q25 90C22 90C35 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Computer ScienceStanford UniversityStanfordUSA
  2. 2.Department of Management Science and Engineering and, by courtesy, Electrical EngineeringStanford UniversityStanfordUSA

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