Finding Largest Common Substructures of Molecules in Quadratic Time

  • Andre Droschinsky
  • Nils KriegeEmail author
  • Petra Mutzel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10139)


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 \(\mathsf{NP}\)-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 \(\mathcal {O}(\varDelta n^2)\) in outerplanar graphs on n vertices with maximum degree \(\varDelta \). 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.


Molecular Graph Input Graph Maximal Solution Subgraph Isomorphism Outerplanar Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceTechnische Universität DortmundDortmundGermany

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