Speed Optimization of AMG

Now that AMG's results are getting better, I've started to look at improvements to the speed. At the moment, it's about 10 times as slow as OMG - probably due to my use of an inferior canonical checker (ie: not nauty).

One obvious improvement has been to avoid extending molecules with too many or too few hydrogens. Previously, the hydrogens were only checked for the leaves - that is, at the final step. It is possible to prune the generation tree earlier, if you make two simple assumptions (see image).

The min extension checks the smallest possible way to add all the remaining atoms to the molecule - which is just a tree. This gives the maximum number of hydrogens that could be added at this point. The max extension does the opposite, checking the case where all remaining atoms are added (at their maximum valence) which has the effect of effectively removing hydrogens.

So, the number of implicit hydrogens for a partial structure is added or removed by these two bounds, and the target hydrogen count is checked to see if it lies in this range. The effect is to prune branches of the generation tree before they even need to be checked for canonicity or other expensive tests:

The tree here is arranged so that the number of hydrogens decreases from left to right - although this may not be the order the structures are actually visited. The dashed lines indicate how the side branches are pruned away.

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Adamantane, Diamantane, Twistane

After cubane, the thought occurred to look at other regular hydrocarbons. If only there was some sort of classification of chemicals that I could use look up similar structures. Oh wate, there is . Anyway, adamantane is not as regular as cubane, but it is highly symmetrical, looking like three cyclohexanes fused together. The vertices fall into two different types when colored by signature: The carbons with three carbon neighbours (degree-3, in the simple graph) have signature (a) and the degree-2 carbons have signature (b). Atoms of one type are only connected to atoms of another - the graph is bipartite . Adamantane connects together to form diamondoids (or, rather, this class have adamantane as a repeating subunit). One such is diamantane , which is no longer bipartite when colored by signature: It has three classes of vertex in the simple graph (a and b), as the set with degree-3 has been split in two. The tree for signature (c) is not shown. The graph is still bipartite accordin

1,2-dichlorocyclopropane and a spiran

As I am reading a book called "Symmetry in Chemistry" (H. H. Jaffé and M. Orchin) I thought I would try out a couple of examples that they use. One is 1,2-dichlorocylopropane : which is, apparently, dissymmetric because it has a symmetry element (a C2 axis) but is optically active. Incidentally, wedges can look horrible in small structures - this is why: The box around the hydrogen is shaded in grey, to show the effect of overlap. A possible fix might be to shorten the wedge, but sadly this would require working out the bounds of the text when calculating the wedge, which has to be done at render time. Oh well. Another interesting example is this 'spiran', which I can't find on ChEBI or ChemSpider: Image again courtesy of JChempaint . I guess the problem marker (the red line) on the N suggests that it is not a real compound? In any case, some simple code to determine potential chiral centres (using signatures) finds 2 in the cyclopropane structure, and 4 in the

General Graph Layout : Putting the Parts Together

An essential tool for graph generation is surely the ability to draw graphs. There are, of course, many methods for doing so along with many implementations of them. This post describes one more (or perhaps an existing method - I haven't checked). Firstly, lets divide a graph up into two parts; a) the blocks, also known as ' biconnected components ', and b) trees connecting those blocks. This is illustrated in the following set of examples on 6 vertices: Trees are circled in green, and blocks in red; the vertices in the overlap between two circles are articulation points. Since all trees are planar, a graph need only have planar blocks to be planar overall. The layout then just needs to do a tree layout on the tree bits and some other layout on the embedding of the blocks. One slight wrinkle is shown by the last example in the image above. There are three parts - two blocks and a tree - just like the one to its left, but sharing a single articulation point. I had

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