The Discretizable Distance Geometry Problems (DDGP) are Distance Geometry Problems (DGP) whose search space can be discretized and represented by a binary tree which can be explored by a branch-and-prune (BP) algorithm. It turns out that this combinatorial search space possesses many interesting symmetry properties studied in the last decade. This talk will present a new algorithm that effectively leverages these properties and may provide a considerable speed-up with respect to the classic BP algorithm. Moreover, the talk will also cover a discussion about stationary points of the smooth stress function for this subclass of DGPs.