[r-t] 147 TDMM

[Alexander Holroyd]

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

For each pair of plans in the list (ie a few million pairs), do the 
following.  "Rotate" one of the pair through all 60 possible starting 
rows.  (Your plans are already in standard form, aren't they?)  For each 
such rotation, compare the two plans.  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.  The simple splice 
itself may be described by saying what methods X and Y are, and what the 
set of leads is, in "standard form" (i.e. rotated to it's smallest version 
in lexicographic order).

After this is done for all pairs, the set of simple splices that arise had 
better be what exactly we expect, i.e. things like "2 copies of the 
Cambride-Beverley 6-lead splice".

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.

Now we want to analyse the clusters.  Any cluster that contains a 
single-method extent can be removed from the game, because these we 
(hopefully) completely understand.  For the others, it would be desirable 
to nominate a "standard representative" plan from each cluster - the basic 
plan which then gets embelished with various simple splices to form the 
other members of the cluster.  I'm not sure whether there is a canonical 
way to do this in general, but one natural thing that springs to mind is 
to list, for each cluster, the plans that have the smallest number of 
methods, and see by hand which of these (if there is more than one) is the 
most "natural".

Then one can summarize the whole thing by listing, for each cluster, its 
standard representative, and the list of all simple splices it involves. 
I suspect such a list would be quite manageable.

Ander