I asked a little while ago on Twitter about whether there’s a given (searchable) name for a class of problem, and I realize given the answers that there isn’t enough information in 140 characters.

So here’s an attempt to state the problem more clearly:

Suppose you are told there are points in , but not their positions, and are also given a list of Euclidean distances between some (or all) pairs of those points. You are asked to determine whether the distances are feasible or not.

For example, suppose I say there are four points in a plane, , , and , and that the distance , , and ; if I’ve done the sketching right, those distances are feasible for points in a plane. If however , the distances are infeasible.

Another way to frame an example, I guess, is to simply ask is it possible that there are four points in , , , and , and that the distance , , , and ?

What I’m wondering is whether this class of geometric constraint satisfaction problems has a particular name that one might, you know, look up. Like the Boolean satisfiability problem and the knapsack problem have special names all their own.