A6struct-The field programmable gate-array (FPGA) has become an important technology in VLSI ASIC designs. In the past a few years, a number of heuristic algorithms have been proposed for technology mapping in lookup-table (LUT) based FPGA designs, but none of them guarantees optimal solutions for general Boolean networks and Little is known about how far their solutions are away h m the optimal ones. This paper presents a theoretical breakthrough which shows that the LUT-based FPGA technology mapping problem for depth minimization can be solved optimally in polynomial time. A key step in our algorithm is to compute a minimum height K-feasible cut in a network, which is solved optimally in polynomial time based on network flow computation. Our algorithm also effectively minimizes the number of LUT's by maximizing the volume of each cut and by several post-processing operations. Based on these results, we have implemented an LUT-based FPGA mapping package called FlowMap. We have tested FlowMap on a large set of benchmark examples and compared it with other LUT-based FPGA mapping algorithms for delay optimization, including Chortle-d, MIS-pgadelay, and DAG-Map. FlowMap reduces the LUT network depth by up to 7% and reduces the number of LUT's by up to 50% compared to the three previous methods.
In this paper, we study the area and depth tradeoff in lookup-table (LUT) based FPGA technology mapping. Starting from a depth-optimal mapping solution, we perform a sequence of depth relaxation operations and area-minimizing mapping procedures to produce a set of mapping solutions for a given design with smooth area and depth trade-off. As the core of the area minimization step, we have developed a polynomial time optimal algorithm for computing an area-minimum mapping solution without node duplication for a K-bounded general Boolean network, which makes a significant step towards complete understanding of the general area minimization problem in FPGA technology mapping. The experimental results on MCNC benchmark circuits show that our solution sets outperform the solutions produced by most existing mapping algorithms in terms of both area and depth minimization.
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