An improved algorithm for performance optimal technology mapping with retiming in LUT-based FPGA design

A novel algorithm, named SeqMapII, of technology mapping with retiming for optimal clock period for K-LUT based FPGAs was recently proposed by P. Pan and C.L. Liu (1996). The time complexity of their algorithm, however, is O(K³n⁴ log(Kn²) log n) for sequential circuits with n gates, which is too high for medium and large size designs in practice. In this paper, we present three strategies to improve the performance of that approach:(1) efficient label update with single K-cut computation based on the monotone property of labels that we showed for sequential circuits, (2) a novel approach for the K-cut computation in partial flow networks, which are much smaller in practice, (3) SCC (strongly connected component) partition to further speedup the algorithm. In practice, our algorithm works in O(Kn³logn) time and O(Kn) space according to our experimental results. It is 2×10⁴ times faster than SeqMapII-opt for computing optimal solutions and 2 times faster than SeqMapII-heu which uses very small expanded circuits as a heuristic