Efficient parallel algorithms for optical computing with the DFT primitive

Abstract

The optical computing technology offers new challenges to the algorithm designers since it can perform an n-point DFT computation in only unit time. Note that DFT is a non-trivial computation in the PRAM model. We develop two new models, DFT-VLSIO and DFT-Circuit, to capture this characteristic of optical computing. We also provide two paradigms for developing parallel algorithms in these models. Efficient parallel algorithms for many problems including polynomial and matrix computations, sorting and string matching are presented. The sorting and string matching algorithms are particularly noteworthy. Almost all of these algorithms are within a polylog factor of the optical computing (VLSIO) lower bounds derived in [BR87] and [TR90].