Cyclo-Static Dataflow Graphs (CSDFGs in short) is a static model commonly used to describe communications between processes. It is increasingly considered for modeling applications executed by many-core architectures; their static analysis becomes thus essential for developing efficient compile- time optimization. This paper aims to develop efficient algorithms to approxi- mately solve two main difficult problems: the determination of the maximum throughput of a CSDFG and the optimization of the buffer sizes with a minimum required throughput. They are both based on a new characterization of feasible periodic schedules. A polynomial-time algorithm is deduced to evaluate the maximum throughput of a periodic schedule, providing a lower bound of the maximum throughput of the CSDFG. A new model for the optimization of the buffer sizes with a minimum required throughput based on integer linear pro- gramming is also developed, leading to a new algorithm to solve it approximately. Our algorithms are successfully compared with other academic solutions through representative benchmarks.