Euclidean Distance Geometry and Applications

@article{Liberti2014EuclideanDG,
  title={Euclidean Distance Geometry and Applications},
  author={Leo Liberti and Carlile Lavor and Nelson Maculan and Antonio Mucherino},
  journal={SIAM Rev.},
  year={2014},
  volume={56},
  pages={3-69}
}
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consist of an incomplete set of distances and the output is a set of points in Euclidean space realizing those given distances. We survey the theory of Euclidean distance geometry and its most important applications, with special emphasis on molecular conformation problems. 
Open research areas in distance geometry
Distance geometry is based on the inverse problem that asks to find the positions of points, in a Euclidean space of given dimension, that are compatible with a given set of distances. We briefly
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