The distance geometry problem (DGP)

Abstract

The fundamental problem of DG, as we have previously stated, is to determine all the coordinates of a set points, in a given geometric space, for which some of the distances are known. Depending on the application, these points can represent stars, reachable points for a robot arm, atoms, or people. Each one of these objects can be represented by a vertex of a graph, and if the distance between them is known, we have an edge connecting the correspondent vertices. Formally, we have the following definition of the Distance Geometry Problem (DGP) [57].