Optimal functional-unit assignment for heterogeneous systems under timing constraint

In high-level synthesis for real-time systems, it typically employs heterogeneous functional-unit types to achieve high-performance and low-cost designs. In the design phase, it is critical to determine which functional-unit type to be mapped for each operation in a given application such that the total cost is minimized while the deadline can be met. For a path or tree structured application, existing approaches can obtain the minimum-cost assignment, called 'optimal assignment', under which the resultant system satisfies a given timing constraint. However, it is still an open question whether there exist efficient algorithms to obtain the optimal assignment for the directed acyclic graph (DAG), or more generally, the data-flow graph with cycles (cyclic DFG). For DAGs, by analyzing the property of the problem, this paper designs an efficient algorithm to obtain the optimal assignments. For cyclic DFGs, we approach this problem with the combination of retiming technique to thoroughly explore the design space. We formulate a Mixed Integer Linear Programming (MILP) model to give the optimal solution. But because of the high degree of its time complexity, we devise a practical algorithm to obtain near-optimal solutions within a minute. Experimental results show the effectiveness of our algorithms. Specifically, compared with existing techniques, we can achieve 25.70 and 30.23 percent reductions in total cost on DAGs and cyclic DFGs, respectively.