Multicasts on WDM all-optical multistage interconnection networks

Wavelength-division multiplexing (WDM) optical networks provide huge bandwidth by allowing multiple data streams to be transmitted simultaneously along the same optical fiber, with each stream assigned a distinct wavelength. A key issue of WDM optical networks is the minimization of the number of wavelengths for realizing a routing request. Let W be the number of wavelengths supported by a WDM optical network. For a routing request R which needs l wavelengths, if l⩽W then R can be realized in one round of routing. However, when l>W, multiple rounds of routing for R are required. In this case, it is important to minimize the number of routing rounds. Multicast transmits a data stream from one input to multiple outputs (one-to-many), a fundamental communication pattern in many applications. We study the problem of minimizing the number of wavelengths and the number of routing rounds for realizing a set R={(u, ν)} of multicasts, where each output ν receives a data stream from exactly one input u, on an n-dimensional WDM all-optical multistage interconnection networks (MINs). For a network with wavelength converters, we show that any set of multicasts can be realized by 2^{[(n-1)/(k+1)]} wavelengths in k rounds of routing. For one round of routing, the upper bound 2^[(n-1)/2] is tight to the lower bound. We also give algorithms for multicasts on a network without wavelength converters. Computer simulation results show that any set of multicasts can be realized in at most two rounds of routing on a network of practical size