The Discretizable Molecular Distance Geometry Problem (DMDGP) is a subclass of the Distance Geometry Problem, which aims to embed a weighted simple undirected graph in a Euclidean space, such that the distances between the points correspond to the values given by the weighted edges in the graph. The search space of the DMDGP is combinatorial, based on a total vertex order that implies symmetry properties related to partial reflections around planes defined by the Cartesian coordinates of three immediate and consecutive vertices that precede the so-called symmetry vertices. Since these symmetries allow us to know a priori the cardinality of the solution set and to calculate all the DMDGP solutions, given one of them, it would be relevant to identify these symmetries efficiently. Exploiting mathematical properties of the vertices associated with these symmetries, we present an optimal algorithm that finds such vertices.

可离散的分子距离几何问题（DMDGP）是距离几何问题的子类，该问题旨在将加权的简单无向图嵌入到欧几里得空间中，这样，点之间的距离对应于坐标中加权边给出的值。图形。DMDGP的搜索空间是基于总顶点顺序的组合，该总顶点顺序隐含与对称平面相关的对称性，该对称性是围绕在所谓对称顶点之前的三个立即和连续顶点的笛卡尔坐标所定义的平面周围的部分反射的。由于这些对称性使我们能够先验地知道解集的基数并计算所有DMDGP解（给定其中一个），因此有效识别这些对称性将很重要。