Efficient Parallel Random Sampling : Vectorized, Cache-Efficient, and Online

We consider the problem of sampling n numbers from the range { 1,… , N } without replacement on modern architectures. The main result is a simple divide-and-conquer scheme that makes sequential algorithms more cache efficient and leads to a parallel algorithm running in expected time O ( n / p +log p ) on p processors, i.e., scales to massively parallel machines even for moderate values of n . The amount of communication between the processors is very small (at most O (log p )) and independent of the sample size. We also discuss modifications needed for load balancing, online sampling, sampling with replacement, Bernoulli sampling, and vectorization on SIMD units or GPUs.