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There exist several practical applications that require high-speed shortest-path computations. In many situations, especially in embedded applications, an field programmable gate array (FPGA)-based accelerator for computing the shortest paths can help to achieve high performance at low cost. This study presents an FPGA-based distributed architecture for solving the single-source shortest-path problem in a fast and efficient manner. The proposed architecture is based on the Bellman-Ford algorithm adapted to facilitate early termination of computation. One of the novelties of the architecture is that it does not involve any centralised control and the processing elements (PEs), which are identical in construction, operate in perfect synchronisation with each other. The functional correctness of the design has been verified through simulations and also in actual hardware. It has been shown that the implementation on a Xilinx Virtex-5 FPGA is more than twice as fast as a software implementation of the algorithm on a high-end general-purpose processor that runs at an order-of-magnitude faster clock. The speed-up offered by the design can be further improved by adopting an interconnection topology that maximises the data transfer rate among the PEs.