Hi,
could you please explain your problem more in detail?
What is your problem, optimization? It is related with the embedding of
finite metrics over finite graph? That is, what do you mean with
euclidean separation of nodes? Something like w(i, j) is the distance
between Rome and Venice or w(i, j) can be any real non negative value
that defines a distance?

If the latter is the case and you're problem is optimization you're
looking to an optimization over the metric polytope; on the other hand
if the former is the case and you're problem may be optimization over a
network graph (possibly a network flow problem).

If you specify deeper your problem maybe i can be a bit more helpful.

Giacomo.


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