Algorithms for the identification of three-dimensional maximal common substructures

Two algorithms are described for the identification of the maximal substructures common to two (or more) three-dimensional chemical structures, where a substructure consists of a set of atoms and the associated interatomic distances. The algorithm of Crandell and Smith involves a breadth-first tree search procedure in which substructures are expanded as they are shown to be common to all of the molecules under consideration. The clique-detection algorithm involves the identification of cliques in the correspondence graph linking matching atoms and interatomic distances in pairs of structures that are being compared. This second algorithm is shown to be substantially faster in operation than the Crandell and Smith algorithm when applied to structures taken from the Cambridge Crystallographic Data Bank, and an extension to the algorithm is described that allows it to be used for the identification of the maximal substructure common to arbitrary numbers of molecules.

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