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Most of the existing work on FPGA acceleration of Convolutional Neural Network (CNN) focus on employing a single strategy (algorithm, dataflow, etc.) across all the layers. Such an approach does not achieve optimal latency on complex and deep CNNs. Emerging CNNs have diverse per-layer computation characteristics including parallelism, arithmetic intensity, locality, and memory footprint. Per-layer strategy selection and fine-grained tuning are required to achieve low end-to-end latency. However, specialized hardware modules dedicated to each layer limit the per-layer utilization and adversely affect end-to-end latency. In this paper, we address these problems by an algorithm-architecture co-optimization framework, DYNAMAP, consisting of (1) a unified hardware overlay that can be reused across layers, supporting dynamic mapping of all three families of popular convolution algorithms, and further allowing flexible dataflow switching to maximize hardware utilization for each layer; (2) a novel software Design Space Exploration (DSE) flow that customizes the hardware overlay and chooses optimal strategy mapping. We show that the algorithm mapping space increases exponentially with network depth, and while the optimal algorithm selection problem is NP-hard in general, by exploiting the series-parallel structure of CNN models, we demonstrate a polynomial-time solution for optimal algorithm mapping. DYNAMAP is optimized for any CNN, including those having diverse computation and memory requirements across the layers. We demonstrate DYNAMAP using two state-of-the-art CNNs - GoogleNet and Inception-V4. The generated accelerators achieve up to $2.8\times$ and $1.4\times$ speedups, respectively, wrt inference latency compared with the state-of-the-art FPGA implementations.