Suppose we have a linear molecule of n atoms (i. e., the molecule can be embedded in the real line). Further, suppose that S ⊂ {1, 2, . . . , n} × {1, 2, . . . n} is a set of indices identifying pairs of atoms whose distances are known. That is, if (i, j) ∈ S then the distance between atom i and atom j, dij > 0, is known. Let the unknowns x1, . . . , xn represent the locations of the atoms on the real line and define.