40 J. Chem. Inf. Model., Vol. 50, No. 1, 2010 CLARK Figure 4. Stepwise assignment of a common numbering system, for a fragmentation tree consisting of 4 molecules. fragments comprising the node are extracted, and clustered in a greedy fashion. Starting with the ﬁrst set of coordinates as the ﬁrst cluster, each subsequent set of coordinates is added to the same cluster as any fragment for which its coordinates can be superposed with an rmsd of less than 0.1 Å or to a new cluster if none. The common atom mapping scheme derived in the previous step is used to enforce pairwise atom matches. If there is more than one cluster, which can occur when fragments have layout degrees of freedom such as rotational symmetry or aliphatic chains, the cluster with the largest number of members is selected. The ﬁrst set of coordinates in this cluster is used as the deﬁnitive reference. For fragments that were found in the same cluster, a translation/rotation/inversion is sufﬁcient to map to the reference coordinates. This transformation is applied simul- taneously to all fragments belonging to a particular molecule, not just the fragment under consideration. Fragments which are not in the reference cluster require more sophisticated treatment. In each case, the whole molecule for the fragment is resubmitted to the depiction layout algorithm, with a special constraint: the coordinates for the fragment are submitted as a preblock, which forces the layout algorithm to construct the rest of the 2D molecule around the predeﬁned fragment, whose coordinates are taken from the reference fragment. This process has been previ- ously described for drawing molecules with common scaf- folds, and is used to obtain coordinates which are optimal for the collection of molecules, if not necessarily each individual molecule.6 The coordinates from all of the fragments corresponding to the whole molecule are updated accordingly. Figure 5 illustrates these distinct steps. The fragmentation patterns for 3 molecules are shown, each of which has been subjected to unconstrained depiction layout. Consider the fragments in column (b), which form a single node in the resulting tree, and are directly descended from the common root fragment shown in (a). The fragments (1,b) and (2,b) can be superposed onto each other, and so they are part of the same cluster of size 2. Fragment (3,b) cannot be superposed, and so it is assigned to its own cluster of size 1. The largest cluster consists of (1,b) and (2,b). The coordinates of (1,b) are used as the reference point. For the fragment (2,b), the coordinates are superposed onto the reference. For fragment (3,b), the coordinates are obtained by redepiction, using the reference coordinates as the preblock. Figure 6