Relaxed Models for Adversarial Streaming: The Advice Model and the Bounded Interruptions Model
This work addresses the space efficiency problem for streaming algorithm designers by introducing incremental models that reduce computational overhead in adversarial environments.
The paper tackles the high space cost of adversarially robust streaming algorithms by proposing two intermediate models—the advice model and the bounded interruptions model—to interpolate between oblivious and adversarial settings, resulting in robust algorithms with significantly improved space complexity.
Streaming algorithms are typically analyzed in the oblivious setting, where we assume that the input stream is fixed in advance. Recently, there is a growing interest in designing adversarially robust streaming algorithms that must maintain utility even when the input stream is chosen adaptively and adversarially as the execution progresses. While several fascinating results are known for the adversarial setting, in general, it comes at a very high cost in terms of the required space. Motivated by this, in this work we set out to explore intermediate models that allow us to interpolate between the oblivious and the adversarial models. Specifically, we put forward the following two models: (1) *The advice model*, in which the streaming algorithm may occasionally ask for one bit of advice. (2) *The bounded interruptions model*, in which we assume that the adversary is 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 the oblivious model. This allows us to design robust algorithms with significantly improved space complexity compared to what is known in the plain adversarial model.