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There are an increasing number of high- performance networks that provision dedicated channels through circuit-switching or MPLS/GMPLS techniques to support large- scale data transfer. The available bandwidths on these dedicated links vary over time and therefore efficient bandwidth scheduling algorithms are needed to improve the utilization of network resources and satisfy diverse user requirements. Based on different path and bandwidth constraints, we formulate four instant scheduling problems for a data transfer request: (i) variable path with variable bandwidth (VPVB), (ii) fixed path with variable bandwidth (FPVB), (iii) variable path with fixed bandwidth (VPFB), and (iv) fixed path with fixed bandwidth (FPFB), with the common objective to minimize transfer end time for a given data size. We design an optimal algorithm for each of these scheduling problems with polynomial- or pseudo- polynomial-time complexity with respect to the network size and total number of time slots in a bandwidth reservation table.