# 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.

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## 334 Citations

Open research areas in distance geometry

- MathematicsArXiv
- 2016

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…

A Cycle-Based Formulation for the Distance Geometry Problem

- Mathematics, Computer Science
- 2020

This work proposes and test a new mathematical programming formulation based on the incidence between cycles and edges in the given graph, where the edges are realized as straight segments of length equal to the edge weight.

On the estimation of unknown distances for a class of Euclidean distance matrix completion problems with interval data

- Mathematics, Computer Science
- 2020

Realizing Euclidean distance matrices by sphere intersection

- Computer ScienceDiscret. Appl. Math.
- 2019

Distance Geometry on the Sphere

- MathematicsJCDCGG
- 2015

This paper generalizes a theorem of Godel about the case where the distances are spherical geodesics, and discusses a method for realizing cliques geodesically on a K-dimensional sphere.

Discretization orders and efficient computation of cartesian coordinates for distance geometry

- Computer ScienceOptim. Lett.
- 2014

New discretization assumptions that are weaker than previously proposed ones are discussed, and a greedy algorithm is presented for an automatic identification of discretized orders to motivate the development of a new method for computing point coordinates.

A constrained interval approach to the generalized distance geometry problem

- Mathematics, Computer ScienceOptim. Lett.
- 2020

This paper presents a new approach to the generalized distance geometry problem, based on a model that uses constraint interval arithmetic, and gives some computational experiments that illustrate the better performance of the proposed approach, compared to others from the literature.

Recent Advances on Oriented Conformal Geometric Algebra Applied to Molecular Distance Geometry

- ChemistrySystems, Patterns and Data Engineering with Geometric Calculi
- 2021

Oriented Conformal Geometric Algebra was recently applied to Molecular Distance Geometry, where we want to determine 3D protein structures using distance information provided by Nuclear Magnetic…

The Isomap Algorithm in Distance Geometry

- Computer ScienceSEA
- 2017

This work starts from a simple observation, namely that Isomap can also be used to provide approximate realizations of weighted graphs very eciently, and then derive and benchmark six new heuristics.

Fisher information distance: a geometrical reading?

- Computer Science, MathematicsDiscret. Appl. Math.
- 2015

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