As far as I know, multidimensional scaling requires a matrix of pairwise distances between the data points to be available. What if I only have distances between some pairs of points, but not all of them?

In some cases, in a Euclidean space, one can compute a unique embedding (up to rigid transforms and reflections) without having to know the distances between all pairs of points. In the case illustrated below, we do not need the distances $\|\mathbf{A} - \mathbf{D}\|$, $\|\mathbf{B} - \mathbf{E}\|$ and $\|\mathbf{C} - \mathbf{F}\|$ to compute an embedding. Are there algorithms that can cope with a partially available distance matrix?