  Finding the common structural features of two molecules is a fundamental task
in cheminformatics. Most drugs are small molecules, which can naturally be
interpreted as graphs. Hence, the task is formalized as maximum common subgraph
problem. Albeit the vast majority of molecules yields outerplanar graphs this
problem remains NP-hard.
  We consider a variation of the problem of high practical relevance, where the
rings of molecules must not be broken, i.e., the block and bridge structure of
the input graphs must be retained by the common subgraph. We present an
algorithm for finding a maximum common connected induced subgraph of two given
outerplanar graphs subject to this constraint. Our approach runs in time
$\mathcal{O}(\Delta n^2)$ in outerplanar graphs on $n$ vertices with maximum
degree $\Delta$. This leads to a quadratic time complexity in molecular graphs,
which have bounded degree. The experimental comparison on synthetic and
real-world datasets shows that our approach is highly efficient in practice and
outperforms comparable state-of-the-art algorithms.
