\setminus \{v\}}} \text{error}_{uw}(x),$$ where $N(v)$ denotes the neighborhood ([*i.e.*]{}the set of incident vertices) of $v$.

In each iteration a new neighbor solution is computed for an edge $\{v,w\}$. To this end, we apply a force-based approach that takes the edge lengths to their neighbors and the edge length of $\{v,w\}$ into account. The idea is to model the local system similarly to the spring embedder model [@eades1984] and the force-directed algorithm by Fruchterman and Reingold [@fruchterman1991]. The difference to those algorithms is that we have to deal with an interval for the length of an edge. In our local force optimization step, we only change the positions of $v$ and $w$ while keeping adjacent vertices fixed.

We say an edge $\{v,w\}$ is *violating* its distance constraint if the error$_{vw}(x)$ is larger than $10^{-9}$ (and not exactly 0 due to numerical reasons). In our spring model only the violating edges account for a repulsive or attractive force, while the other edges do not take part in the force calculation. In our model each spring has its equilibrium state in an interval that corresponds to the interval of the respective edge it models.

For an optimization on edge $\{v,w\}$, the forces acting 