A Polynomial-time Metric for Outerplanar Graphs

Graphs are mathematical structures that are capable of representing relational data. In the chemoinformatics context, they have become very popular for the representation of molecules. However, a lot of operations on graphs are NP-complete, so no efficient algorithms that can handle these structures exist. In this paper we focus on outerplanar graphs, a subclass within general graphs. Most molecular graphs are outerplanar. We define a metric on outerplanar graphs that is based on finding the maximal common subgraph and we present an algorithm that runs in polynomial time. Having an efficiently computable metric on molecules can improve the virtual screening of molecular databases significantly.