A Framework for Adversarially Robust Streaming Algorithms

We investigate the adversarial robustness of streaming algorithms. In this context, an algorithm is considered robust if its performance guarantees hold even if the stream is chosen adaptively by an adversary that observes the outputs of the algorithm along the stream and can react in an online manner. While deterministic streaming algorithms are inherently robust, many central problems in the streaming literature do not admit sublinear-space deterministic algorithms; on the other hand, classical space-efficient randomized algorithms for these problems are generally not adversarially robust. This raises the natural question of whether there exist efficient adversarially robust (randomized) streaming algorithms for these problems.

In this work, we show that the answer is positive forvarious important streaming problems in the insertion-onlymodel, including distinct elements and more generally Fpestimation, Fp-heavy hitters, entropy estimation, and others. For all of these problems, we develop adversarially robust (1 +ε)-approximation algorithms whose required spacematches that of the best known non-robust algorithms upto a poly(log n, 1/ε) multiplicative factor (and in some caseseven up to a constant factor). Towards this end, we developseveral generic tools allowing one to efficiently transform anon-robust streaming algorithm into a robust one in variousscenarios.