Query Evaluation by Circuits

In addition to its theoretical interest, computing with circuits has found applications in many other areas such as secure multi-party computation and outsourced query processing. Yet, the exact circuit complexity of query evaluation had remained an unexplored topic. In this paper, we present circuit constructions for conjunctive queries under degree constraints. These circuits have polylogarithmic depth and their sizes match the polymatroid bound up to polylogarithmic factors. We also propose a definition of output-sensitive circuit families and obtain such circuits with sizes matching their RAM counterparts.