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.

The Molecular Distance Geometry Problem consists in finding the positions inof the atoms of a molecule, given some of the inter‐atomic distances. We show that under an additional requirement on the given distances this can be transformed to a combinatorial problem. We propose a Branch‐and‐Prune algorithm for the solution of this problem and report on very promising computational results.