Technology mapping for field-programmable gate arrays using integer programming

We show that the FPGA technology mapping problem can be efficiently implemented as a mixed integer linear programming (MILP) problem which generates truly optimal mappings. The MILP approach can handle a wide variety of FPGA logic block architectures. We present a compact MILP formulation for logic blocks based on lookup tables (LUTs) multiplexers. We also show that the MILP formulation can be easily modified to modified to optimize area, delay, or a combination of both. We demonstrate that moderately large benchmark circuits can be mapped in a reasonable time using the MILP approach directly. For larger circuits, we propose a technique of partitioning a circuit prior to mapping, which drastically reduces the computation time with little or no loss in optimality.