— This work considers the problem of transmitting multiple compressible sources over a network with minimum cost. The problem is complicated by the fact that the description of the feasible rate region of distributed source coding problems typically has a number of constraints that is exponential in the number of sources that renders general purpose solvers inefficient. We present a framework in which these problems can be solved efficiently by exploiting the structure of the feasible rate regions coupled with dual decomposition and subgradient methods.