On the Exact Solution of the Distance Geometry with Interval Distances in Dimension 1

A GPU approach to distance geometry in 1D: an implementation in C/CUDA

“…When the BP algorithm mentioned in the Introduction is employed for the solution of paradoxical DGP instances in dimension 1 [9], a binary tree containing all possible vertex positions can be recursively constructed, and the valid realizations can be selected at the very end when positions are computed for the last vertex v n ∈ V . Our paradoxical instances have the particularity of solely executing the branching phase of the algorithm until a leaf node of the tree is reached; it is only at this point that the pruning mechanism is invoked, where the only distance not used for branching, the distance related to the edge {1, n}, is verified.…”

“…The Branch-and-Prune (BP) algorithm was proposed in [4] for a subclass of DGP instances that admit the discretization of their search space. In the 1-dimensional case, this algorithm can be employed under the much weaker assumption that the graph G is connected [9]. In this case, in fact, a vertex order on V , which ensures that every vertex v has at least one predecessor u (exception made for the first vertex in the order), can be easily constructed [8].…”