Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finding Largest Common Substructures of Molecules in Quadratic Time   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.

14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin