Network Coding: An Optimization Approach

We consider the problem of computing the capacity of a coded, multicast network over a small alphabet. We introduce a novel approach to this problem based on mixed integer programming. As an application of our approach, we recover, extend and refine various results that were previously obtained with case-by-case analyses or specialized arguments, giving evidence of the wide applicability of our approach and its potential. We also provide two simple ideas that reduce the complexity of our method for some families of networks. We conclude the paper by outlining a research program we wish to pursue in the future to investigate the capacity of large networks affected by noise, based on the approach proposed in this paper.