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(G₁, G₂)

• Input: Two graphs G₁ and G₂.
• Question: What is the largest subgraph of G₁ isomorphic to a subgraph of G₂?

The associated decision problem, i.e., given G₁, G₂ and an integer k, deciding whether G₁ contains a subgraph of at least k vertices isomorphic to a subgraph of G₂ 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

References

• Michael R. Garey and David S. Johnson (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman. ISBN 0-7167-1045-5.  A1.4: GT48, pg.202.