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Computational Optimization and Applications

, Volume 52, Issue 3, pp 609–627 | Cite as

Comparing SOS and SDP relaxations of sensor network localization

Article

Abstract

We investigate the relationships between various sum of squares (SOS) and semidefinite programming (SDP) relaxations for the sensor network localization problem. In particular, we show that Biswas and Ye’s SDP relaxation is equivalent to the degree one SOS relaxation of Kim et al. We also show that Nie’s sparse-SOS relaxation is stronger than the edge-based semidefinite programming (ESDP) relaxation, and that the trace test for accuracy, which is very useful for SDP and ESDP relaxations, can be extended to the sparse-SOS relaxation.

Keywords

Sensor network localization Semidefinite programming relaxation Sum of squares relaxation Individual trace 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WashingtonSeattleUSA
  2. 2.CMUC, Department of MathematicsUniversity of CoimbraCoimbraPortugal

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