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An all-optical approach to achieve finer bandwidth granularity is to time division multiplex low capacity circuits on each wavelength channel and to switch time-wavelength slots within the network. In such a Time-Wavelength-Switched- Network (TWSN), the Time-Wavelength-Space-Routers (TWSRs) are configured to change their routing pattern on a time slot basis. Another kind of time slotted network proposed in the literature is the Time-Wavelength-Interleaved Network (TWIN), which eliminates time switching within the network by using a non-reconfigurable core and an intelligent edge utilizing a fast tunable laser to emulate fast switching. A drawback of the TWIN network is that it assigns a unique wavelength to each node in the network. Thus it requires a total of W = N wavelengths for an N-node network and hence is not scalable. In this paper we propose to design a wavelength-constrained (i.e., W <; N) TWIN network with no switching (TWIN-NS) by using a multicasting strategy. We also propose a variant of the TWIN network which possesses switching capabilities only at the edge nodes (TWIN-ES), and compare the performances of these TWIN networks to that of the TWSN. We present integer linear programs and heuristic algorithms to solve the connection scheduling problem in the TWSN and the TWIN, and investigate the benefits of having a fast reconfigurable switch as opposed to a non-reconfigurable core.