Euclidean Distance Matrices, Semidefinite Programming, and Sensor Network Localization

The fundamental problem of distance geometry, F P DG , involves the characterization and study of sets of points based only on given values of (some of) the distances between pairs of points. This problem has a wide range of applications in various areas of mathematics, physics, chemistry, and engineering. Euclidean Distance Matrices, EDM , play an important role in F P DG . They use the squared distances and provide elegant and powerful convex relaxations for F P DG . These EDM problems are closely related to graph realization, GRL ; and graph rigidity, GRD , plays an important role. Moreover, by relaxing the embedding dimension restriction, EDM problems Department of Mathematics & Statistics, University of Windsor. Research supported by Natural Sciences Engineering Research Council of Canada. Department of Management Sciences, University of Waterloo, and Universität zu Köln, Institut für Informatik, Pohligstrasse 1, 50969 Köln, Germany. Research supported by Natural Sciences Engineering Research Council of Canada, MITACS, and the Humboldt Foundation. Dipartimento di Ingegneria dell’Impresa Università degli Studi di Roma “Tor Vergata” Via del Politecnico, 1 00133 Rome, Italy. Research supported by Natural Sciences Engineering Research Council Canada, MITACS, and AFOSR.