  Two vertices $u$ and $v$ of an undirected graph $G$ are strongly resolved by
a vertex $w$ if there is a shortest path between $w$ and $u$ containing $v$ or
a shortest path between $w$ and $v$ containing $u$. A vertex set $R$ is a
strong resolving set for $G$ if for each pair of vertices there is a vertex in
$R$ that strongly resolves them. The strong metric dimension of $G$ is the size
of a minimum strong resolving set for $G$. We show that a minimum strong
resolving set for an undirected graph $G$ can be computed efficiently if and
only if a minimum strong resolving set for each biconnected component of $G$
can be computed efficiently.
