Skip to main content

Generation : Overview

To sum up the previous post flood; generation of constitutional isomers from the elemental formula can be done by generating all partitions of the total 'free' valence of the heavy atoms. The overall scheme is shown here:

(click for bigger, as usual). So, for each formula, multiple partitions can be made, and each of these makes multiple sub-partitions, and each of these correspond to one or more molecules.

Now, I won't pretend that any of this is particularly novel. I am no doubt re-expressing the problem of generating all possible molecules in a slightly different way. Having tried (and failed) to implement published methods, this was the best I could come up with.

I suspect that there are many improvements that could be made to the algorithm, and the implementation of it. Getting something that works, even in a limited way, seems like progress, however :)


Anonymous said…
Hi Gilleain,
looking at the figures of the partitions it becomes clear that the deterministic generation of all possible isomers is an embarrassingly parallel problem.

Each partition can be handled as single problem and that means if you have 10000 partitions and 10000 CPUs (CUDA TESLA, SiCortex Supercomputer)
you could dedicate each problem to one CPU core or thread.

The problem with the old monolithic CDK deterministic isomer generator code was, that the (FORTRAN style) code can be easily parallelized, but the canonizer was extremely slow. So even having n-CPUs at hand would
not solve the speed problem.

But I think for the molecular space below 500 Da the fully parallelized version could solve most of the problems in a sufficient time frame (if above problem would be fixed and n-CPUs would be available).

gilleain said…
Hi Tobias,

You are right, it does look like it can be easily run in parallel.

One important thing, though, is that the number of partitions grows much more slowly than the number of structures - for the CnH2n series, the number of partitions is (42, 627, 5604) for C=(10, 20, 30). There are a LOT more C30H60 structures than 5604...

So, it might be that the natural 'unit' would be smaller - but the problem at the moment is that it is still checking within the set of children of each partition for isomorphism.

Still, it is a good idea.

Anonymous said…
"number of partitions is (42, 627, 5604) for C=(10, 20, 30). There are a LOT more C30H60 structures than 5604..."

....well you are right, lets say below 200-300 Da. There we go, the isomorphism tester is still the bottleneck, so a fast isomorphism tester version is still needed.

If you take a CUDA TESLA C1060 with 240 GPU like streaming processors and 80 GFlop/s double precision fp (or 1000 single precision floating point precision) it should be still faster than an 8 core (16 thread) Intel Core I7 which has around 40 GFLOP/s (double precision) and 80 GFLOPs (SP). The CUDA bottleneck can be the transfer from the CPU to the GPU.

In conclusion a massively parallelized code version distributing each partition to each core, using an ultrafast isomorphism tester, together with a versatile good-list and bad-list handler, bundled with with a proper NMR and MS and IR handler would be the way to go :-)

If I go to Wolfram Alpha and ask for the number of all isomers in the universe it still tells me: 42


Popular posts from this blog

Generating Dungeons With BSP Trees or Sliceable Rectangles

So, I admit that the original reason for looking at sliceable rectangles was because of this gaming stackoverflow question about generating dungeon maps. The approach described there uses something called a binary split partition tree (BSP Tree) that's usually used in the context of 3D - notably in the rendering engine of the game Doom. Here is a BSP tree, as an example:

In the image, we have a sliced rectangle on the left, with the final rectangles labelled with letters (A-E) and the slices with numbers (1-4). The corresponding tree is on the right, with the slices as internal nodes labelled with 'h' for horizontal and 'v' for vertical. Naturally, only the leaves correspond to rectangles, and each internal node has two children - it's a binary tree.

So what is the connection between such trees and the sliceable dual graphs? Well, the rectangles are related in exactly the expected way:

Here, the same BSP tree is on the left (without some labels), and the slicea…

Listing Degree Restricted Trees

Although stack overflow is generally just an endless source of questions on the lines of "HALP plz give CODES!? ... NOT homeWORK!! - don't close :(" occasionally you get more interesting ones. For example this one that asks about degree-restricted trees. Also there's some stuff about vertex labelling, but I think I've slightly missed something there.

In any case, lets look at the simpler problem : listing non-isomorphic trees with max degree 3. It's a nice small example of a general approach that I've been thinking about. The idea is to:
Given N vertices, partition 2(N - 1) into N parts of at most 3 -> D = {d0, d1, ... }For each d_i in D, connect the degrees in all possible ways that make trees.Filter out duplicates within each set generated by some d_i. Hmm. Sure would be nice to have maths formatting on blogger....

Anyway, look at this example for partitioning 12 into 7 parts:

At the top are the partitions, in the middle the trees (colored by degree) …

Common Vertex Matrices of Graphs

There is an interesting set of papers out this year by Milan Randic et al (sorry about the accents - blogger seems to have a problem with accented 'c'...). I've looked at his work before here.

[1] Common vertex matrix: A novel characterization of molecular graphs by counting
[2] On the centrality of vertices of molecular graphs

and one still in publication to do with fullerenes. The central idea here (ho ho) is a graph descriptor a bit like path lengths called 'centrality'. Briefly, it is the count of neighbourhood intersections between pairs of vertices. Roughly this is illustrated here:

For the selected pair of vertices, the common vertices are those at the same distance from each - one at a distance of two and one at a distance of three. The matrix element for this pair will be the sum - 2 - and this is repeated for all pairs in the graph. Naturally, this is symmetric:

At the right of the matrix is the row sum (∑) which can be ordered to provide a graph invarian…