A remark on global positioning from local distances.
Finding the global positioning of points in Euclidean space from a local or partial set of pairwise distances is a problem in geometry that emerges naturally in sensor networks and NMR spectroscopy of proteins. We observe that the eigenvectors of a certain sparse matrix exactly match the sought coordinates. This translates to a simple and efficient algorithm that is robust to noisy distance data.
Singer
Amit
A
Department of Mathematics, Program in Applied Mathematics, Yale University, New Haven, CT 06520, USA. amit.singer@yale.edu
D000465:Algorithms; D002947:Cities; D008377:Maps as Topic; D015233:Models, Statistical; D014481:United States