Efficient enumeration of monocyclic chemical graphs with given path frequencies

BACKGROUND: The enumeration of chemical graphs (molecular graphs) satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics because it leads to a variety of useful applications including structure determination and development of novel chemical compounds. RESULTS: We consider the problem of enumerating chemical graphs with monocyclic structure (a graph structure that contains exactly one cycle) from a given set of feature vectors, where a feature vector represents the frequency of the prescribed paths in a chemical compound to be constructed and the set is specified by a pair of upper and lower feature vectors. To enumerate all tree-like (acyclic) chemical graphs from a given set of feature vectors, Shimizu et al. and Suzuki et al. proposed efficient branch-and-bound algorithms based on a fast tree enumeration algorithm. In this study, we devise a novel method for extending these algorithms to enumeration of chemical graphs with monocyclic structure by designing a fast algorithm for testing uniqueness. The results of computational experiments reveal that the computational efficiency of the new algorithm is as good as those for enumeration of tree-like chemical compounds. CONCLUSIONS: We succeed in expanding the class of chemical graphs that are able to be enumerated efficiently.