Graphs of Trees of Graphs (ok, just timings again)

Line-graphs of search-trees of molecular-graphs, that is. I should also point out that I am not using the cutting-edge development version of OMG, but rather the commit 30b08250efa4.... - sadly, I don't have java7 on this machine, so I can't run the latest versions.

Anyway, it doesn't make much difference for the alkanes and alkenes. Here are the times in miliseconds, and log(t in ms) for CnH2n and CnH2n+2. Click for bigger, as always:

Clearly AMG (in blue) is significantly slower than OMG (in red), roughly by 10 times. On the other hand, the picture is surprisingly different if we add in a few oxygens:

Weird, but I suspect that this kind of problem has been fixed in more recent versions of OMG. User "mmajid" seems to have been doing some interesting experiments with using bliss instead of nauty, multithreading, and semicanonical checking.

Comments

Tobias said…

Hi,
just a general heads up, these are great improvements,
considering its a "tiny" version update.

C7H16O2 from 510 sec --> 4 sec = 127 fold faster
C6H14O3 from 387 sec --> 5 sec = 77x speed increase.

That is great news. Actually even stuff like C7H16O3
that was a time-out in the old version runs now in 27 seconds.
Think about a parallel version with 32 threads and it runs in 1 sec.
...and from there another 100-fold increase to match MOLGEN-Demo.

Anyway, I think its great and if some graph people would chime in
and contribute code it surely would even go faster :-)

Cheers
Tobias

12 December 2012 at 11:03

The Gale-Ryser Theorem

This is a small aside. While reading a paper by Grüner, Laue, and Meringer on generation by homomorphism they mentioned the Gale-Ryser (GR) theorem. As it turns out, this is a nice small theorem closely related to the better known Erdős-Gallai (EG). So, GR says that given two partitions of an integer ( p and q) there exists a (0, 1) matrix A iff p* dominates q such that the row sum vector r(A) = p and the column sum vector c(A) = q . As with most mathematics, that's quite terse and full of terminology like 'dominates' : but it's relatively simple. Here is an example: The partitions p and q are at the top left, they both sum to 10. Next, p is transposed to get p* = [5, 4, 1] and this is compared to q at the bottom left. Since the sum at each point in the sequence is greater (or equal) for p* than q , the former dominates. One possible matrix is at the top left with the row sum vector to the right, and th...

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 ...

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...

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