Algoritmo de reflexões para o problema de geometria de distâncias discretizável

Abstract

The objective of the Distance Geometry Problem (DGP) is to determine a set of coordinates in a Euclidean space that satisfies a given set of restrictions. The applicability of DGP spreads in several areas, from molecular geometry to robotics. The Branch-and-Prune (BP) algorithm is one of the most important algorithms in the DGP literature. Basically, the BP algorithm represents the DGP search space as a binary tree and reduces it to the resolution of a sequence of quadratic systems. However, BP can perform a large number of repeated operations, unnecessarily increasing computational effort. In view of this problem, the present work purposes an alternative to reduce the number of operations performed through symmetries easily identifiable in DGP graph representation.