Dataflow modeling is a highly regarded method for the design of embedded systems. Measuring the performance of the associated analysis and compilation tools requires an efficient dataflow graph generator. This paper presents a new graph generator for Phased Computation Graphs (PCG), which augment Cyclo-Static Dataflow Graphs with both initial phases and thresholds. A sufficient condition of liveness is first extended to the PCG model. The determination of initial conditions minimizing the total amount of initial data in the channels and ensuring liveness can then be expressed using Integer Linear Programming. This contribution and other improvements of previous works are incorporated in Turbine, a new dataflow graph generator. Its effectiveness is demonstrated experimentally by comparing it to two existing generators, DFTools and SDF3.