given distance interval, the algorithm either prolongates or shortens the edge length such that it is exactly as long as the upper or lower bound given by the distance interval, respectively. We only accept the change if we reduce the local edge error. If we change the length of an edge $\{v,w\}$, we lock the other incident edges of $v$ and $w$ for the remainder of the current iteration to prevent an oscillating effect. We perform a maximum of iterations or less if there is no improvement between two successive iterations. Pseudocode of the method is shown as Algorithm \[alg:simple-local\] in Appendix \[sub:simple-local\].

Intervals with Confidence Values: wiMDGP {#sub:algo-wiMDGP}
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Some distances can be measured more accurately than others in common biomolecular experimental methods. To account for this, we add a confidence to each interval. Such a confidence states how certain it is that the actual distance is contained in this interval, leading us to the following problem definition:

\[Weighted Interval Distance Geometry (Optimization) Problem (wiDGP)\] Let a simple undirected graph $G = (V,E)$, a distance interval function $d = [l,u]$, a confidence function $p: E \rightarrow \mathbb{R}$, and an integer $k > 0$ be given. Then minimize the following 