A remark on global positioning from local distances

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79 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)9507-9511
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number28
StatePublished - Jul 15 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General


  • Distance geometry
  • Eigenvectors
  • Multidimensional scaling
  • Sensor networks


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