I am considering a network with the max flow problem in a particular situation. I have a set of flows which should pass a certain node A and and another set of flows which should avoid A and pass through another node B. The flows can cross each other at any other arbitrary node. Under what category of network flow problems should this be considered?
Allocating flows in a network while avoiding a particular node
graphs;network flow
Flows with more than one thing flowing are known as multicommodity flows.The basic definitions assume that every thing can flow through every vertex and edge. However, the standard way of solving these problems is linear programming and you could easily modify the normal multicommodity flow program to deal with your situation, just by substituting zero for the appropriate variables.