  Let $\mathcal{A}$ be a set of positive numbers. A graph $G$ is called an
$\mathcal{A}$-embeddable graph in $\mathbb{R}^d$ if the vertices of $G$ can be
positioned in $\mathbb{R}^d$ so that the distance between endpoints of any edge
is an element of $\mathcal{A}$. We consider the computational problem of
recognizing $\mathcal{A}$-embeddable graphs in $\mathbb{R}^1$ and classify all
finite sets $\mathcal{A}$ by complexity of this problem in several natural
variations.
