Parallel algorithms based on expander graphs for optical computing

We consider the task of interconnecting processors to realize efficient parallel algorithms. We propose interconnecting processors using certain graphs called expander graphs, which can provide fast communication from any group of processors to the rest of the network. We show that these interconnections would result in a number of efficient parallel algorithms for sorting, routing, associative memory, and fault-tolerance networks. As the interconnections based on expander graphs are global and irregular, we reason that optical interconnections are preferred to electronic and propose implementation of these interconnections using the programmable optoelectronic multiprocessor architecture.