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In this paper, we introduce a novel FPGA architecture with memristor-based reconfiguration (mrFPGA). The proposed architecture is based on the existing CMOS-compatible memristor fabrication process. The programmable interconnects of mrFPGA use only memristors and metal wires so that the interconnects can be fabricated over logic blocks, resulting in significant reduction of overall area and interconnect delay but without using a 3D die-stacking process. Using memristors to build up the interconnects can also provide capacitance shielding from unused routing paths and reduce interconnect delay further. Moreover we propose an improved architecture that allows adaptive buffer insertion in interconnects to achieve more speedup. Compared to the fixed buffer pattern in conventional FPGAs, the positions of inserted buffers in mrFPGA are optimized on demand. A complete CAD flow is provided for mrFPGA, with an advanced P&R tool named mrVPR that was developed for mrFPGA. The tool can deal with the novel routing structure of mrFPGA, the memristor shielding effect, and the algorithm for optimal buffer insertion. We evaluate the area, performance and power consumption of mrFPGA based on the 20 largest MCNC benchmark circuits. Results show that mrFPGA achieves 5.18x area savings, 2.28x speedup and 1.63x power savings. Further improvement is expected with combination of 3D technologies and mrFPGA.