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This paper first reviews some theoretical results in error-tolerant graph matching that were obtained recently. The results include a new metric for error-tolerant graph matching based on maximum common subgraph, a relation between maximum common subgraph and graph edit distance, and the existence of classes of cost functions for error-tolerant graph matching. Then some new optimal algorithms for error-tolerant graph matching are discussed. Under specific conditions, the new algorithms may be significantly more efficient than traditional methods.

Error-tolerant graph matching: A formal framework and algorithms