Document

**Published in:** LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass through the stream and using as little space as possible.
Motivated by the importance of data privacy, we develop differentially private streaming algorithms under the continual release setting, where the union of outputs of the algorithm at every timestamp must be differentially private. Specifically, we study the fundamental 𝓁_p (p ∈ [0,+∞)) frequency moment estimation problem under this setting, and give an ε-DP algorithm that achieves (1+η)-relative approximation (∀ η ∈ (0,1)) with polylog(Tn) additive error and uses polylog(Tn)⋅ max(1, n^{1-2/p}) space, where T is the length of the stream and n is the size of the universe of elements. Our space is near optimal up to poly-logarithmic factors even in the non-private setting.
To obtain our results, we first reduce several primitives under the differentially private continual release model, such as counting distinct elements, heavy hitters and counting low frequency elements, to the simpler, counting/summing problems in the same setting. Based on these primitives, we develop a differentially private continual release level set estimation approach to address the 𝓁_p frequency moment estimation problem.
We also provide a simple extension of our results to the harder sliding window model, where the statistics must be maintained over the past W data items.

Alessandro Epasto, Jieming Mao, Andres Munoz Medina, Vahab Mirrokni, Sergei Vassilvitskii, and Peilin Zhong. Differentially Private Continual Releases of Streaming Frequency Moment Estimations. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 48:1-48:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{epasto_et_al:LIPIcs.ITCS.2023.48, author = {Epasto, Alessandro and Mao, Jieming and Medina, Andres Munoz and Mirrokni, Vahab and Vassilvitskii, Sergei and Zhong, Peilin}, title = {{Differentially Private Continual Releases of Streaming Frequency Moment Estimations}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {48:1--48:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-263-1}, ISSN = {1868-8969}, year = {2023}, volume = {251}, editor = {Tauman Kalai, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.48}, URN = {urn:nbn:de:0030-drops-175513}, doi = {10.4230/LIPIcs.ITCS.2023.48}, annote = {Keywords: Differential Privacy, Continual Release, Sliding Window, Streaming Algorithms, Distinct Elements, Frequency Moment Estimation} }

Document

Track A: Algorithms, Complexity and Games

**Published in:** LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Many modern parallel systems, such as MapReduce, Hadoop and Spark, can be modeled well by the MPC model. The MPC model captures well coarse-grained computation on large data - data is distributed to processors, each of which has a sublinear (in the input data) amount of memory and we alternate between rounds of computation and rounds of communication, where each machine can communicate an amount of data as large as the size of its memory. This model is stronger than the classical PRAM model, and it is an intriguing question to design algorithms whose running time is smaller than in the PRAM model.
In this paper, we study two fundamental problems, 2-edge connectivity and 2-vertex connectivity (biconnectivity). PRAM algorithms which run in O(log n) time have been known for many years. We give algorithms using roughly log diameter rounds in the MPC model. Our main results are, for an n-vertex, m-edge graph of diameter D and bi-diameter D', 1) a O(log D log log_{m/n} n) parallel time 2-edge connectivity algorithm, 2) a O(log D log^2 log_{m/n}n+log D'log log_{m/n}n) parallel time biconnectivity algorithm, where the bi-diameter D' is the largest cycle length over all the vertex pairs in the same biconnected component. Our results are fully scalable, meaning that the memory per processor can be O(n^{delta}) for arbitrary constant delta>0, and the total memory used is linear in the problem size. Our 2-edge connectivity algorithm achieves the same parallel time as the connectivity algorithm of [Andoni et al., 2018]. We also show an Omega(log D') conditional lower bound for the biconnectivity problem.

Alexandr Andoni, Clifford Stein, and Peilin Zhong. Log Diameter Rounds Algorithms for 2-Vertex and 2-Edge Connectivity. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 14:1-14:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{andoni_et_al:LIPIcs.ICALP.2019.14, author = {Andoni, Alexandr and Stein, Clifford and Zhong, Peilin}, title = {{Log Diameter Rounds Algorithms for 2-Vertex and 2-Edge Connectivity}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {14:1--14:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.14}, URN = {urn:nbn:de:0030-drops-105906}, doi = {10.4230/LIPIcs.ICALP.2019.14}, annote = {Keywords: parallel algorithms, biconnectivity, 2-edge connectivity, the MPC model} }