Optimal Routing and Channel Assignments for Hypercube Communication on Optical Mesh–like Processor Arrays

This paper considers optimal routing and channel assignment (RCA) schemes to realize hypercube communication on optical mesh–like networks. Specifically, we identify lower bounds on the number of channels required to realize hypercube communication on top of array and ring topologies and develop optimal RCA schemes that achieve the lower bounds on these two topologies. We further extend the schemes to mesh and torus topologies and obtain RCA schemes that use at most 2 more channels than the optimal for these topologies.