C[omp]ute

From: "andrew cooke" <andrew@...>

Date: Sat, 20 Sep 2008 18:54:39 -0400 (CLT)

I have just finished implementing the main core of the algorithm outlined
here - http://www.acooke.org/cute/Identifyin0.html - directly in Java and
it runs in about 8 seconds!

There were two main problems.  First, inferring how Postgres did an
efficient search and, second, implementing that without using too much
memory (my first attempt exhausted the heap so I now have a slight 
tradeoff, which uses a sort to avoid creating more memory structures and
so adds a log term to the big-O).  It's easiest to describe both together,
by outlining the final solution, but in practice I the development had two
distinct steps.

So, as in the prototype code, I generate candidate pairs by matching small
fragments of the DNA.  More exactly: I take 25 fragments, each 8 bits,
from each individual and I categorise two individuals as a candidate pair
if they have at least 3 fragments in common.

So, in psuedocode, I do the following:

 generate a table of fragments[individual_idx][fragment_idx]
 generate a table of counts[individual1_idx][individual2_idx] = 0

 for each column of fragments in turn:
   sort the table column containing the fragments;
   scan the sorted column:
     for all fragments with the same value:
       increment the counts associated with the pairs of individuals
               that share that fragment value;
     if any count == 3:
       if the "bit distance" between the pair is < 3000:
         add the pair for that count to the graph;

And I need to repeat this 6 times with different sets of fragments (the
number of identified pairs after each set is 8116, 9623, 9935, 9988, 9998,
9999).

Instead of sorting each column of fragments the scan could be direct, but
you would need to have a separate memory structure to record which
individuals were associated with which values (for this amount of data I
suspect the log pays for itself in the simplification (reduced constant
cost) that the sorted data introduces).

Also, Java has no direct support for sorting bytes (the fragments) with
keys.  I could have wrapped everything in objects, but it was more compact
(and probably faster) to bit-pack the DNA fragment and the individual
index together in a single integer (obviously the DNA has to occupy the
more significant bits for the sorting to give the corrected order).

I am going to look for a graph library now to finish this off.

8 seconds is pretty good.  When I started out I was looking at many hours;
even the optimized Python/SQL code took 30 min...

Andrew

PS  My initial attempt at searching the hashes was to do a depth first
search trying to find common fragments for each pair in turn.  While this
would have fitted well within a constraint programming framework (see my
posts here over the last week or two when I was looking at Choco and
Gecode) it was, in retrospect, completely stupid - a huge amount of time
is spent exhaustively searching irrelevant pairs.  The direct scan
described above is much more efficient, but it's not yet clear to me how
the two approaches are related.  Is there some way in which the direct
scan with counting is a dual of the search?  Or does some kind of
optimisation of the search eventually reduce it to the scan?  I don't see
how either of those pan out, but haven't looked at the CP techniques in
any detail yet.