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 …

We discuss a discretization-based solution approach for a classic problem in global
optimization, namely the distance geometry problem (DGP). We focus our attention on a …

What do clocks, wireless devices, atoms, and submarines have in common? They move: the
clocks move time forward (so to speak), wireless devices usually move on a plane (like an …

Data are often represented as graphs. Many common tasks in data science are based on
distances between entities. While some data science methodologies natively take graphs as …

When a weighted graph is an instance of the Distance Geometry Problem (DGP), certain
types of vertex orders (called discretization orders) allow the use of a very efficient, precise …

Background The determination of protein structures satisfying distance constraints is an
important problem in structural biology. Whereas the most common method currently …

Laman graphs model planar frameworks that are rigid for a general choice of distances
between the vertices. There are finitely many ways, up to isometries, to realize a Laman …

Abstract Nuclear Magnetic Resonance (NMR) experiments provide distances between
nearby atoms of a protein molecule. The corresponding structure determination problem is …

Considering geometry based on the concept of distance, the results found by Menger and
Blumenthal originated a body of knowledge called distance geometry. This survey covers …

The calculation of the 3D structure of a protein molecule is important because it is
associated to its biological function. Nuclear Magnetic Resonance (NMR) experiments can …