We present a novel algorithm for designing optimal cellular interconnects (OCI's), which can significantly accelerate the communications among processors in single-instruction multiple-data machines with optoelectronic interconnections. We present the foundations of the OCI architecture and show that the optoelectronic OCI is the optimal topology for a space-invariant interconnect pattern. The OCI is optimal in achieving a minimum number of clock cycles per data shift for a given number of optoelectronic links. In addition, our algorithm for designing the OCI is deterministic, whereas previous designs required a trial-and-error procedure.