where the set $V$ of $n$ vertices models the atoms and the set $E$ of $m$ edges their relations. Distance information is given separately for all pairs $\{u,v\} \in S \subseteq V \times V$ by a distance matrix $D \in \mathbb{R}_{\geq 0}^{n \times n}$. For this purpose $d_{vw}$ denotes the distance between vertices $v$ and $w$—or is set to `nil` if the distance is unknown (for pairs $\notin S$). We are interested in finding an embedding of $G$ into $\mathbb{R}^3$, [*i.e.,* ]{}3D coordinates for the vertices, that respects the distances for $S$. This problem is known as (3D) *distance geometry problem* (DGP). In line with previous work, we account for inexact distance information due to measurement errors by introducing an interval in which the actual distance is contained. This modified DGP is called *interval distance geometry problem* [@liberti2014survey]:

\[Interval Distance Geometry Problem (iDGP)\] Let a simple undirected graph $G = (V,E)$, a distance interval function $d = [l,u]$ with $d: E \rightarrow \mathbb{R}^2$, and an integer $k > 0$ be given. Then determine whether there is an embedding $x : V \rightarrow \mathbb{R}^k$ such that $$\label{eq:iDGP}
        \forall \{v,w\} \in E: l_{vw} \leq \lVert x_v - x_w \rVert \leq u_{vw},$$ where 