Minimal Network Coding for Multicast
  We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize the number of packets that undergo network coding. We also propose a decentralized algorithm to construct capacity achieving multicast codes when the processing at some nodes is restricted to routing. The proposed algorithms can be coupled with existing decentralized schemes to achieve minimum cost muticast. 
Kapil Bhattad, Niranjan Ratnakar, Ralf Koetter, and Krishna R.   Narayanan