I have a set of points on the two-dimensional plane, but their locations are not given to me. I am given the distance between some pairs of the points. However, I only know these differences for some pairs: I don't have every pairwise distance between the objects. I would like an algorithm to output the locations of the points.
The complication is that there could be some errors in the distances provided to me, so I want the algorithm to output a location for each point such that the pairwise distances between those locations match the provided distances as closely as possible.
Could anyone point me towards a method of computing a placement in 2-dimensional Euclidean space that would best solve this problem?
It would be nice to be able to provide hard constraints as well. For instance, I might be given that $C$ is exactly at the point $(1,2)$, or that all of the objects must fit in a $10 \times 10$ square. However, this is not strictly necessary: an algorithm that does not support hard constraints would still be interesting.