Re: [Axiom-developer] Graph Drawing

[Raymond Rogers]

On 03/07/2015 12:18 PM, address@hidden wrote:
> For large graphs, such as Axiom's category/domain/package graph,
> it is a challenge to find a 2D representation. This new algorithm
> seems to attack that problem.
>
> Graph Drawing by High-Dimensional Embedding
> http://www.wisdom.weizmann.ac.il/~harel/papers/highdimensionalGD.pdf
>
>
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Yes, but it's dealing with undirected graphs.  Although taking the graph 
analysis approach vs partitioning is interesting.
I imagine something like counting ancestors and dependants to form a 
graph matrix.  Thus contrary to my normal graphing thoughts the nodes 
have weights instead of edges.  That can be reversed by duality but I 
have a hard time giving meaning to that in this usage.  Anyway: each 
node would have an associated list of (ancestors, dependants) lists.  
Then if that could be expressed in sets of polynomials a Groebner basis 
algorithm might be able to generate partitions; where different lex 
schemes would give different partitions and alternate solutions might 
also lead to different partitions. (?)
In other words: some scheme to make the graphs be directly generated 
from code.
Alternately a simple sort by something like ancestors might be 
informative.  Where nodes having fewer ancestors would be higher in the 
abstraction chain.
Or so such; just random thoughts.

Ray


--
 Two views on life:
life is an art not to be learned by observation.
George Santayana:Interpretations of Poetry and Religion
It's kinda nice to participate in your life
Raymond Rogers