  Given a connected, undirected, simple graph $G = (V, E)$ and $p \le |V|$
pebbles labeled $1,..., p$, a configuration of these $p$ pebbles is an
injective map assigning the pebbles to vertices of $G$. Let $S$ and $D$ be two
such configurations. From a configuration, pebbles can move on $G$ as follows:
In each step, at most one pebble may move from the vertex it currently occupies
to an adjacent unoccupied vertex, yielding a new configuration. A natural
question in this setting is the following: Is configuration $D$ reachable from
$S$ and if so, how? We show that the feasibility of this problem can be decided
in time $O(|V| + |E|)$.
