FRAGMENT HIERARCHIES J. Chem. Inf. Model., Vol. 50, No. 1, 2010 45 Figure 12. Structurally related COX2 inhibitors. 3. Performance. All algorithms described in this work have been implemented in SVL (Scientiﬁc Vector Language), running in MOE (Molecular Operating Environment).12 The total processing time for the data set of DHFR inhibitors described in part 1 (397 compounds) is approximately 16 s, measured on an Intel 2.0 GHz 32-bit processor. The time taken for each step breaks down roughly as follows: initial depiction (4 s), fragment generation (2 s), deriving common mapping (4 s), colligative redepiction (2 s), and branch orientation (4 s). For the COX-2 inhibitors described in part 2 (467 compounds), the total time taken was approximately 50 s, of which 33 s were devoted to deriving the common mapping scheme. The rate limiting steps scale linearly in proportion to the number of input molecules, with the exception of the mapping step, in the presence of symmetry- containing fragments. An abundance of degenerate partial fragments causes the UQO portion of the common mapping algorithm to dedicate additional computational resources to ﬁnding an optimal mapping. This is the principal reason why the COX-2 data set takes longer to analyze than does the DHFR data set, since the DHFR inhibitors are largely based on heterocyclic ring blocks with low symmetry, while the core fragments of the COX-2 inhibitors contain an abundance of substituents, such as phenyl rings, that have rotational symmetry. CONCLUSION A method has been demonstrated for treating scaffold- like fragmentation trees so that common ancestor fragments are depicted and oriented in a consistent way that makes common structural features readily evident to the observing chemist. The algorithm operates without supervision and produces aesthetically desirable results using a combination of new and preexisting techniques. With the molecule layout and orientation method estab- lished, software applications that present fragmentation trees become signiﬁcantly more valuable to medicinal chemists. There is no longer a requirement to sketch the input molecules in any particular way, nor is it necessary to postprocess the structures to elicit insight into the structure- activity information that is encoded in such trees. The value of presenting structural data in this way has been demonstrated, by using high-level and medium-level hierarchical tree views, which combine constrained clustering with activity color-coding, and the ability to examine individual structures that have a common depiction and orientation. Such views are effective ways to examine structure-activity data, and the algorithms that have been described essentially remove the manual effort required to produce them. Use of such visualization and grouping tools can allow the user to make intuitive selections of compounds for further development. For example, if a set of compounds which has balanced activity and diverse structure is necessary for producing a QSAR validation set, either the tree or dendro- gram presentation methods could be used to identify such a subset, either by visual inspection or automated selection. Alternatively, when considering hypothetical new compounds to add to the collection, it may be informative to depict them under the same conditions as for the existing compounds, and insert them into their appropriate locations within the hierarchy according to the ordering scheme used by the visualization method. Examination of the patterns exhibited by neighboring structures may aid in qualitatively assessing the expected properties of the compound. Future research will involve developing new ways to present information-rich, easily comprehensible graphics in a concise area, for example, single computer screen, projected