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Searching for Optimal Orders for Discretized Distance Geometry

The Distance Geometry Problem (DGP) [5] asks whether a simple weighted undirected graph G = (V, E, d) can be embedded in a K-dimensional space so that the distances between vertex pairs, which are given by the edge weights, are preserved. DGP has various applications; one of the most important applications arises in biology, where vertices represent atoms of a given molecule, and distances can be obtained by studying the chemical structure of the molecule, as well as by performing NMR experiments [6]. In this application, the dimension of the space is fixed to K = 3.