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In this paper, we propose a colored multigraph model for the temporarily available wavelengths. Based on this colored multigraph model, a low-cost delay-constrained routing algorithm is proposed by applying the K-shortest-path strategy. The proposed algorithm has the following advantages: (1) finish routing and wavelength assignment in one step; (2) the total cost of lightpath is low; (3) the delay from the source node to the destination node is bounded. Simulation results show that the proposed algorithm works well and achieves satisfactory blocking probability.