Our work focuses on allocating and scheduling a synchronous data-flow (SDF) graph onto a multi-core platform subject to a minimum throughput requirement. This problem has traditionally be tackled by incomplete approaches based on problem decomposition and local search, which could not guarantee optimality. Exact algorithms used to be considered reasonable only for small problem instances. We propose a complete algorithm based on Constraint Programming which solves the allocation and scheduling problem as a whole. We introduce a number of search acceleration techniques that significantly reduce run-time by aggressively pruning the search space without compromising optimality. The solver has been tested on a number of non-trivial instances and demonstrated promising run-times on SDFGs of practical size and one order of magnitude speed-up w.r.t. the fastest known complete approach.