Abstract
BackgroundEnumeration of chemical graphs satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics since it leads to a variety of useful applications including structure determination of novel chemical compounds and drug design.ResultsIn this paper, we consider the problem of enumerating all tree-like chemical graphs from a given set of feature vectors, which is specified by a pair of upper and lower feature vectors, where a feature vector represents the frequency of prescribed paths in a chemical compound to be constructed. This problem can be solved by applying the algorithm proposed by Ishida et al. to each single feature vector in the given set, but this method may take much computation time because in general there are many feature vectors in a given set. We propose a new exact branch-and-bound algorithm for the problem so that all the feature vectors in a given set are handled directly. Since we cannot use the bounding operation proposed by Ishida et al. due to upper and lower constraints, we introduce new bounding operations based on upper and lower feature vectors, a bond constraint, and a detachment condition.ConclusionsOur proposed algorithm is useful for enumerating tree-like chemical graphs with given upper and lower bounds on path frequencies.
Highlights
Development of novel drugs is one of the major goals in chemoinformatics and bioinformatics
We propose a new exact branch-and-bound algorithm for the problem so that all the feature vectors in a given set are handled directly
We cannot use the bounding operation proposed by Ishida et al for the problem ETULF due to upper and lower constraints
Summary
Development of novel drugs is one of the major goals in chemoinformatics and bioinformatics. To achieve this purpose, it is important to investigate common chemical properties over chemical compounds having common structural patterns [1,2,3] and to study methods of enumerating chemical structures satisfying given constraints. Akutsu and Fukagawa [17] formulated the graph pre-image problem as the problem of inferring graphs from the frequency of paths of labeled vertices, which corresponds to the pre-image problem, and proved that the problem is NP-hard even for planar graphs with bounded degrees [17]. Enumeration of chemical graphs satisfying given constraints is one of the fundamental problems in chemoinformatics and bioinformatics since it leads to a variety of useful applications including structure determination of novel chemical compounds and drug design
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