  


Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization
Yichuan Ding (y7dingmath.uwaterloo.ca) Abstract: We study Semidefinite Programming, \SDPc relaxations for Sensor Network Localization, \SNLc with anchors and with noisy distance information. The main point of the paper is to view \SNL as a (nearest) Euclidean Distance Matrix, \EDM, completion problem and to show the advantages for using this latter, well studied model. We first show that the current popular \SDP relaxation is equivalent to known relaxations in the literature for \EDM completions. The existence of anchors in the problem is {\em not} special. The set of anchors simply corresponds to a given fixed clique for the graph of the \EDM problem. We next propose a method of projection when a large clique or a dense subgraph is identified in the underlying graph. This projection reduces the size, and improves the stability, of the relaxation. In addition, viewing the problem as an \EDM completion problem yields better low rank approximations for the low dimensional realizations. And, the projection/reduction procedure can be repeated for other given cliques of sensors or for sets of sensors, where many distances are known. Thus, further size reduction can be obtained. Optimality/duality conditions and a primaldual interiorexterior path following algorithm are derived for the \SDP relaxations We discuss the relative stability and strength of two formulations and the corresponding algorithms that are used. In particular, we show that the quadratic formulation arising from the \SDP relaxation is better conditioned than the linearized form, that is used in the literature and that arises from applying a Schur complement. Keywords: Sensor Network Localization, Anchors, Graph Realization, Euclidean Distance Matrix Completions, Positive Semidefinite Programming Relaxations Category 1: Linear, Cone and Semidefinite Programming Category 2: Combinatorial Optimization (Graphs and Matroids ) Citation: CORR 200623, Department of Combinatorics and Optimization, University of Waterloo Download: [Postscript][PDF] Entry Submitted: 12/14/2006 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  