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Maximum common subgraph isomorphism problem : ウィキペディア英語版 | Maximum common subgraph isomorphism problem In complexity theory, maximum common subgraph-isomorphism (MCS) is an optimization problem that is known to be NP-hard. The formal description of the problem is as follows: Maximum common subgraph-isomorphism(''G''1, ''G''2) * Input: Two graphs ''G''1 and ''G''2. * Question: What is the largest subgraph of ''G''1 isomorphic to a subgraph of ''G''2? The associated decision problem, i.e., given ''G''1, ''G''2 and an integer ''k'', deciding whether ''G''1 contains a subgraph of at least ''k'' vertices isomorphic to a subgraph of ''G''2 is NP-complete. One possible solution for this problem is to build a modular product graph, in which the largest clique represents a solution for the MCS problem. MCS algorithms have a long tradition in cheminformatics and pharmacophore mapping. ==See also==
*Graph isomorphism problem *Subgraph isomorphism problem *Molecule mining *Maximum common edge subgraph problem
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