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

TL;DR

This paper introduces intermediate models for adversarial streaming, namely the advice model and the bounded interruptions model, which allow for more space-efficient algorithms by relaxing the adversarial assumptions.

Contribution

The paper proposes two new models that interpolate between oblivious and fully adversarial streaming, providing reductions and improved algorithms for these settings.

Findings

Reductions from advice and bounded interruptions models to oblivious model.

Existence of algorithms with improved space complexity in these intermediate models.

Both positive and negative results for the proposed models.

Abstract

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.