Data-independences of parallel random access machines

Abstract

We introduce notions of control and communication structures for PRAM’s and relate them to the concept of data-independence. Our main result is to characterize differences between unbounded fanin parallelism (i.e., the complexity classes ACk, k≥1), bounded fanin parallelism (i.e., the classes NCk, k≥1), and sequentialism (i.e., DSPA CE(log n) and LOGDCFL). We express these differences in terms of data-On)dependences of reads from and writes into the global memory of a PRAM. In particular, we obtain the first characterizations of NCk(k≥1) and DSPACE(log n) in terms of PRAM’s. Finally, we introduce a PRAM model with in some sense built-in data-independence and propose it as a tool for the development of data-independent parallel algorithms.