## Abstract

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 for various important streaming problems in the insertion-only model, including distinct elements and more generally $F-p$-estimation, Fp-heavy hitters, entropy estimation, and others. For all of these problems, we develop adversarially robust (1+ϵ)-approximation algorithms whose required space matches that of the best known non-robust algorithms up to a poly(log n, 1/ϵ) multiplicative factor (and in some cases even up to a constant factor). Towards this end, we develop several generic tools allowing one to efficiently transform a non-robust streaming algorithm into a robust one in various scenarios.

Original language | English |
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Title of host publication | PODS 2020 - Proceedings of the 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems |

Publisher | Association for Computing Machinery |

Pages | 63-80 |

Number of pages | 18 |

ISBN (Electronic) | 9781450371087 |

DOIs | |

State | Published - 14 Jun 2020 |

Externally published | Yes |

Event | 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2020 - Portland, United States Duration: 14 Jun 2020 → 19 Jun 2020 |

### Publication series

Name | Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems |
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### Conference

Conference | 39th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems, PODS 2020 |
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Country/Territory | United States |

City | Portland |

Period | 14/06/20 → 19/06/20 |

### Bibliographical note

Publisher Copyright:© 2020 Proceedings of the ACM SIGACT-SIGMOD-SIGART Symposium on Principles of Database Systems. All rights reserved.

### Funding

E. Yogev is funded by the ISF grants 484/18, 1789/19, Len Blavat-nik and the Blavatnik Foundation, and The Blavatnik Interdisciplinary Cyber Research Center at Tel Aviv University. R. Jayaram and D. Woodruff are supported by the National Science Foundation under Grant No. CCF-1815840. This work was done (in part) in the Simons Institute for the Theory of Computing.

Funders | Funder number |
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Blavatnik Foundation | |

National Science Foundation | CCF-1815840 |

Directorate for Computer and Information Science and Engineering | 1815840 |

Israel Science Foundation | 1789/19, 484/18 |

Tel Aviv University |

## Keywords

- adversarial robustness
- databases
- distinct elements
- frequency moments
- heavy hitters
- streaming algorithms