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Streaming algorithms are typically analyzed in the oblivious setting, wherewe assume that the input stream is fixed in advance. Recently, there is agrowing interest in designing adversarially robust streaming algorithms thatmust maintain utility even when the input stream is chosen adaptively andadversarially as the execution progresses. While several fascinating resultsare known for the adversarial setting, in general, it comes at a very high costin terms of the required space. Motivated by this, in this work we set out toexplore intermediate models that allow us to interpolate between the obliviousand the adversarial models. Specifically, we put forward the following twomodels:  (1) *The advice model*, in which the streaming algorithm may occasionally askfor one bit of advice.  (2) *The bounded interruptions model*, in which we assume that the adversaryis only partially adaptive.  We present both positive and negative results for each of these two models.In particular, we present generic reductions from each of these models to theoblivious model. This allows us to design robust algorithms with significantlyimproved space complexity compared to what is known in the plain adversarialmodel.

Relaxed Models for Adversarial Streaming: The Advice Model and the Bounded Interruptions Model