Recent Developments in Parallel Pseudorandom Number Generation

We summarize some of the recent developments of our research group and of other groups in the design and analysis of pseudorandom number generators for massively parallel computers. The three parallelization techniques we will consider in detail for mapping pseudorandom streams onto distinct parallel processes are: 1. Splitting maximal-period generators' full period into nonoverlapping subse-quences, one for each parallel process. 2. Finding parameterized families of generators and distributing a unique parameter value for the generator used on each parallel process. 3. Finding generators with statistically similar full-period equivalence classes and distributing one equivalence class to each parallel process.