Breadth-first search approach to enumeration of tree-like chemical compounds

Molecular enumeration plays a basic role in the design of drugs, which has been studied by mathematicians, computer scientists, and chemists for quite a long time. Although many researchers are involved in developing enumeration algorithms specific to drug design systems, molecular enumeration is still a hard problem to date due to its exponentially increasing large search space with larger number of atoms. To alleviate this defect, we propose efficient algorithms, BfsSimEnum and BfsMulEnum to enumerate tree-like molecules without and with multiple bonds, respectively, where chemical compounds are represented as molecular graphs. In order to reduce the large search space, we adjust some important concepts such as left-heavy, center-rooted, and normal form to molecular tree graphs. Different from many existing approaches, BfsSimEnum and BfsMulEnum firstly enumerate tree-like compounds by breadth-first search order. Computational experiments are performed to compare with several existing methods. The results suggest that our proposed methods are exact and more efficient.