Optimal-Complexity Optical Router

In the past years, electronic routers have had trouble keeping up with the increase in optical fiber capacity. As their power consumption has grown exponentially and already exceeds standards, it seems that an alternative solution is mandatory. Many have suggested all-optical routers as an alternative. However, these are deemed too complex, especially given the need to implement both switching and buffering, even though their fundamental complexity has apparently never been analyzed. In this paper, we study the number of fundamental optical components (2 times 2 switches and fiber delay lines) needed to emulate ideal routers. We first demonstrate that an N times N router with a buffer size of B per port needs at least thetas(N log(N B)) components, and then build a construction that achieves this lower bound. On the way, we also present an optical buffer construction of size B that works with thetas(log(B)) components, which is also shown to be a lower bound. Finally, we generalize this result to different router architectures and scheduling disciplines.