Communication and Memory Efficient Testing of Discrete Distributions

We study distribution testing with communication and memory constraints in the following computational models: (1) The em one-pass streaming model where the goal is to minimize the sample complexity of the protocol subject to a memory constraint, and (2) A em distributed model where the data samples reside at multiple machines and the goal is to minimize the communication cost of the protocol. In both these models, we provide efficient algorithms for uniformity/identity testing (goodness of fit) and closeness testing (two sample testing). Moreover, we show nearly-tight lower bounds on (1) the sample complexity of any one-pass streaming tester for uniformity, subject to the memory constraint, and (2) the communication cost of any uniformity testing protocol, in a restricted `one-pass' model of communication.