The Non-Bijective Triangular score

The Non-Bijective triangular score is a variation of the Triangular score. Actually its formulation is the same, but when using non-bijective formulation, the correspondence does not need to be sequential, neither monotone, neither bijective, that is, different atoms from one structure can be associated with the same atom of the second structure.

The non-bijective formulation must be used for general alignments for which one does not expect sequentiality, as for alignments of ligands, or of parts of proteins including the side chains. Actually the non-bijective algorithm is very versatile in such a way that one could align any kind of structure.

A important side-effect of the use of the non-bijective approach is the speed by which the correspondence, and thus the alignment, can be computed. For instance, since for each atom one must identify only the nearest atom of the other structure, an algorithm was devised that has a cost, in practice, linearly dependent on the size of the smallest of the two structures being compared [ref]. This can be very significant for database comparisons or for difficult alignment requiring many initial points.