If this condition is not satisfied, we can exclude that the fragments in F (u) could match synthons of the synthon reaction. Because we can run this heuristic already on the unlabeled forest F (u), we can omit a large number of cut sets without ever looking at their enumerated labeled forests. The example shown in Fig. illustrates the efficiency of the connector heuristic, as 409 out of 411 valid decompositions can be eliminated in this way. Please note that we can again use the method for fast superset testing in enumerated libraries to perform the necessary substructure searches.