Does anyone have any good pointers to >2d graph theory?
In particular I've been wrapping my brain around thinking
of Vadim Antonov's approach of a "stacked network" of
several identical interconnected planes, where each plane
is a set of vertices (routers) interconnected by lines
(T3s back then...). In particular, I think the maths
are easier if one treats vertices as line segments instead
of points -- each point on the line segment is an interface.
The vertices are interconnected by plane-segments and each
line-segment in the plane-segment is a tranmissions line
(of 2.5, 10, or 40 Gbps, for example).
In essence this is a simple case of extending various network
elements outwards at a common angle.
For the multiple-fibre case (e.g. multi-conduit, or
multi-fibre-per-conduit), we extend various network elements
outwards at a common angle orthogonal to the previous angle.
Now we have oblong polyhedra interconnecting 2d polygons.
This all assumes that we abstract away a dimension, so we
can consider a single topological "point" rather than revealing
the inner-workings of that "point" to the rest of the network.
I've found some supercomputer references which aren't really
very helpful except for routing within any given vertex; I've
also found some really cool graphical stuff and pure math
stuff which is more pretty than helpful, like
http://members.aol.com/Polycell/uniform.html
Of course, any suggestions that I really don't want/need
to learn this stuff because it's the wrong way to look
at a network, and that keeping a graph as 2d as possible
is a long-term sensible approach, is also welcome.
Sean.
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