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Efficient scheduling for heterogeneous fractional lambda switching (FlambdaS) networks is required but challenging. A heterogeneous network implies bandwidth mismatch between links of varied bit rates. Moreover, when non-immediate forwarding (NIF) is used in FlambdaS, it increases the scheduling complexity exponentially, while decreasing the blocking probability. Thus, NIF scheduling presents a serious challenge for an algorithm to be used in a large heterogeneous FlambdaS network. In this paper, an efficient scheduling algorithm that is combined with a flexible forwarding scheme is presented. The algorithm provides a full scheduling solution for an end-to-end request in heterogeneous FlambdaS networks. Furthermore, the algorithm has linear complexity in single-channel networks and quadratic complexity in multiple-channel WDM networks.