On the Discretization of Distance Geometry: Theory, Algorithms and Applications

Over the last years, my research activity has mainly been focused on Distance Geometry (DG). Differently from the classical Euclidean Geometry, DG solely relies on distances, and one of its main problems consists in identifying point positions by exploiting information about inter-point distances. This problem is known in the scientific literature as the DG Problem (DGP). This research topic is strongly multidisciplinary, and has applications in several disciplines, such as structural biology, robotics, motion adaptation, to name a few. My research on the DGP is focused on a particular class of DGP instances for which the discretization of the search space can be performed with no (or, in some cases, with a reasonably small) loss of information. This allows us to employ a Branch-and-Prune (BP) algorithm for a systematic exploration of the search tree obtained with the discretization. In collaboration with national and international partners, we developed the theory of the Discretizable DGP (DDGP), and we studied the different facets of the problem, while considering its different applications. More recently, we have been extending the DGP to dynamical problems, and tackling motion adaptation problems by a novel DGP-based problem formulation.