The Adversarial Robustness of Sketching and Streaming Algorithms

2026-07-15

AI Summary

This work systematically investigates the robustness of streaming algorithms under adversarial adaptive inputs, where future data depend on prior algorithmic outputs—a setting in which classical sketching and streaming methods fail to guarantee correctness. By integrating differential privacy, cryptographic techniques, and linear sketching theory, we develop novel robust algorithms for both insertion-only and turnstile (insertion-deletion) streams. We uncover deep connections between adversarial robustness, differential privacy, and cryptography, and delineate the feasibility boundaries for fundamental tasks such as norm estimation, frequency moment approximation, and heavy-hitter detection under adaptive adversaries. Our results establish that achieving robustness often necessitates polynomial space or high-dimensional sketches, revealing inherent limitations, while also providing efficient solutions for frequency-based statistics and outlining promising directions for future research.

Abstract

Sketching and streaming algorithms are vital for handling massive datasets. While classical methods guarantee correctness on fixed inputs, they often fail with adaptive inputs, where future data depends on past algorithm outputs. This is common in settings such as optimization, databases, finance, and network monitoring. This monograph surveys recent advances in adversarial robustness, including techniques for insertion-only streams, connections to differential privacy, and cryptographic methods that achieve adversarial robustness. We also discuss fundamental limitations, especially for linear sketches and streams with insertions and deletions, where robustness often requires polynomial space or sketching dimension. Throughout, we explore core problems like adaptively answering queries for optimization problems, norm estimation, frequency moments, and heavy hitters, and highlight emerging tools and open challenges at the intersection of streaming, sketching, privacy, and adversarial robustness.

Problem

• adversarial robustness
• streaming algorithms
• sketching algorithms
• adaptive inputs
• data streams

Innovation

• adversarial robustness
• streaming algorithms
• sketching
• differential privacy
• cryptographic methods