We study weighted graphs that can be embedded in the plane in such a way as to preserve
an edge's weight as Euclidean distance between its two endpoints. Such questions arise in
a variety of layout problems. In automatic graph drawing, for example, vertices are to be
placed so as to approximate desired pairwise distances. The analogous 3-d problem arises
in the distance geometry approach to molecular modeling, where edge weights are
approximate distance measurements. We introduce the concept of elastic embeddability …