The exposition is not very clear. What exactly do you mean when you say "No edges will be communicated over the network, only half of the nodes."? I'm puzzled, because a few sentences later, you claim "The only network IO that would be required would be sending each edge value to its respective node in Q."; so the edge values are actually communicated?
From what I've understood, what you're suggesting is that for every node in a layer, you colocate the edge on the same machine?
