[r-t] 147 TDMM

[Richard Smith]

Alexander Holroyd wrote:

> Here is an idea for an automated method for analysing the 
> plans.

Thanks for that!  I've now coded it up.

> Specifically, look to see whether the two plans are 
> identical except that one is obtained from the other by 
> replacing some set of leads all of method X with all 
> method Y.  If so, say that there is a "simple splice" 
> between the two plans.

This means that replacing all of one method with the other 
counts as a 'simple splice'.  I think I like that in 
principle, though I don't think it's likely to very useful 
in practice.  So I've actually made the code ignore these 
trivial 30-lead splices.

> We now have a graph, whose vertices (nodes) are the plans, and whose edges 
> (links) are the simple splices.  Break this graph up into its connected 
> components, or "clusters".  Each cluster is a group of plans all of which 
> communicate with each other via simple splices.
>
> For a start I would like to know how many clusters there are.

I've started by testing it on the 396 plans that only 
include surprise methods (i.e. from the 41) as I'm fairly 
confident I know what's going to be found there.  Here, we 
find 21 clusters of which 10 are simple.

The simple components contain the following methods:

   1.  Ws Ad
   2.  Ne Ab Lf Ro Wm St Bo Hu
   3.  No
   4.  Bm Bc
   5.  Wk
   6.  Ip Nf Cm Pr Su He Bv Bk Yo Du
   7.  Sa Wo
   8.  Li Co
   9.  Ke
   10. Ak Ct Nb Wh Cl Mu Ch Nw Mo Cu Lo We

(If we allow the '30-lead splice', then these all merge into 
a single cluster.)

The 11 interesting clusters are:

   1.  Ws-No-Ne/Bo grid splices
   2.  Ip-Cm-Ne/Bo grid splices
   3.  Ip-Cm-Yo compound splices
   4.  Bo-Su-Du/Yo compound splices + Cm (3 leads of Bo)
   5.  Bo-Su-Du compound splice (15 leads of Bo)
   6.  Bo-Su-Du compound splices + Cm (6 leads of Bo)
   7.  Nb-Cl/Cu-Sa grid splices
   8.  Nb-Cl-Ak compound splices
   9.  Sa-Mu-Nw compound splice (15 leads of Sa)
   10. Sa-Mu-Nw/Ak compound splices + Cl (6 leads of Sa)
   11. Sa-Mu-Nw/Ak compound splices + Cl (3 leads of Sa)

The full analysis of the all 4614 plans should be finished 
shortly.

RAS