Cyclo-Static DataFlow Graphs (CSDFG in short) is a formalism commonly used to model parallel applications composed by actors communicating through buffers. The liveness of a CSDFG ensures that all actors can be executed infinitely often. This property is clearly fundamental for the design of embedded applications. This paper aims to present first an original sufficient condition of liveness for a CSDFG. Two algorithms of polynomial-time for checking the liveness are then derived and compared to a symbolic execution of the graph. An original method to compute close-to-optimal buffer capacities ensuring liveness is also presented and experimentaly tested. The performance of our methods are comparable to those existing in the literature for industrial applications. However, they are far more effective on randomly generated instances, ensuring their scalability for future more complex applications and their possible implementation in a compiler.