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This work presents Hermes, a depth-optimal LUT based FPGA mapping algorithm. The presented algorithm is based on a new strategy for finding LUTs allowing to find a good LUT in a significantly shorter time compared to the previous methods. The quality of results is improved by enabling LUT re-implementation and by introducing a cost function which encourages input sharing among LUTs. The experimental results show that, on average, the presented algorithm computes 15.5% and 3.5% smaller LUT mappings compared to the ones obtained by FlowMap and CutMap, respectively, using two orders of magnitude less CPU time. The speed of Hermes makes it suitable for running in an incremental manner during logic synthesis.