草图绘制和流算法的对抗鲁棒性
The Adversarial Robustness of Sketching and Streaming Algorithms
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中文总结 AI 辅助
探讨草图绘制和流算法在处理海量数据集时的对抗鲁棒性，综述其最新进展，包括相关技术、与差分隐私联系及加密方法等，讨论基本限制，还探索了核心问题，突出交叉领域的新兴工具与挑战。
中文摘要 AI 辅助
草图绘制和流算法对于处理海量数据集至关重要。经典方法在固定输入上能保证正确性，但面对自适应输入（未来数据依赖过去算法输出）常失效，在优化、数据库、金融和网络监测等场景很常见。本专著综述对抗鲁棒性的最新进展，包括仅插入流的技术、与差分隐私的联系及实现对抗鲁棒性的加密方法。还讨论了基本限制，特别是线性草图和有插入删除的流，其鲁棒性常需多项式空间或草图维度。探讨了如自适应回答优化问题查询、范数估计、频率矩和重尾等核心问题，突出了流、草图、隐私和对抗鲁棒性交叉领域的新兴工具和开放挑战。
英文摘要
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.
