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

Authors Menachem Sadigurschi, Moshe Shechner, Uri Stemmer

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Menachem Sadigurschi
  • Department of Computer Science, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Moshe Shechner
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
Uri Stemmer
  • Blavatnik School of Computer Science, Tel Aviv University, Israel
  • Google Research, Tel Aviv, Israel

Funding

This project was partially supported by the Israel Science Foundation (grant 1871/19) and by Len Blavatnik and the Blavatnik Family foundation.

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Menachem Sadigurschi, Moshe Shechner, and Uri Stemmer. Relaxed Models for Adversarial Streaming: The Bounded Interruptions Model and the Advice Model. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 91:1-91:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.91

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:  
- The bounded interruptions model, in which we assume that the adversary is only partially adaptive. 
- The advice model, in which the streaming algorithm may occasionally ask for one bit of advice. 
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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Streaming, sublinear and near linear time algorithms
Keywords
  • streaming
  • adversarial streaming

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