Finding Largest Common Substructures of Molecules in Quadratic Time

TL;DR

This paper introduces a quadratic-time algorithm for finding the largest common substructure in molecules, modeled as outerplanar graphs, while preserving ring structures, and demonstrates its efficiency on real-world data.

Contribution

The paper presents a novel quadratic-time algorithm for maximum common subgraph detection in outerplanar graphs with ring-preserving constraints, improving efficiency over existing methods.

Findings

Algorithm runs in O(Δ n^2) time for outerplanar graphs.

Outperforms state-of-the-art algorithms on synthetic and real datasets.

Efficiently finds maximum common substructures while maintaining molecular ring integrity.

Abstract

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.