Graph rigidity, unassigned distance geometry and the nanostructure problem

The unassigned distance geometry (UDGP) problem takes as input a list of interpoint distances, d = {dı}, l = 1,..., |d|, and its solution is a set of point positions in a Euclidean space of dimension K. The UDGP is difficult because it requires both the discovery of the underlying graph structure and the embedding of that graph. Recent theoretical results and algorithms based on building up low cost structures from smaller substructures are outlined and application domains are discussed.