function: $$\label{eq:icDGOP}
        \sum_{\{v,w\} \in E} \omega_{vw} \cdot \text{error}_{\{v, w\}}(x),$$ where the weight $\omega_{vw}$ depends on the edge’s confidence value $c_{vw}$.

In order to support wiMDGP, we adapt the maxent-stress algorithm as well as the other two optimization algorithms. For wiMDGP we can use the weights $\omega_{vw}$ from Eq. (\[eq:maxent-stress\]), the maxent-stress optimization problem, as a penalty that increases the error of an edge if the confidence that the distance lies in the interval is high. After some manual parameter tuning, we have chosen the following function to define the weighting factors: $\omega_{vw} \coloneqq 1 + 5\exp^{-5 (1 - c_{vw})},$ where $c_{vw}$ denotes the confidence for edge $\{v,w\}$. This way, the weight of an edge is roughly in the interval $[1, 6]$ and increases rapidly between A confidence between $0$ and $0.6$ only tells us that we cannot be very certain about the distance and thus, the error term should not vary too much. For higher confidence values, we can be quite certain that the distance interval is correct, so we need to penalize the errors of such edges significantly higher. Choosing a larger interval for the weights turned out not to be beneficial in terms of solution quality in preliminary 