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In this paper, we study shortest-path routing in wavelength-routed optical networks with an objective to optimize the average-case running time for path computation. Four fast routing algorithms are proposed for dynamically computing the shortest lightpaths or semilightpaths in a network with or without wavelength converters. To reduce the average-case running time for path computation, sequential search, backward routing, and informed search are used in the algorithm design. Simulation results show that the proposed algorithms can significantly reduce the average-case computational overhead for path computation as compared with existing algorithms.