4 Search Results for "Medina, Andres Munoz"

Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2025.2
Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk)

Authors: Monika Henzinger and Roodabeh Safavi

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We give an introduction into differential privacy in the dynamic setting, called the continual observation setting.
Cite as

Monika Henzinger and Roodabeh Safavi. Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk). In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.2,
  author =	{Henzinger, Monika and Safavi, Roodabeh},
  title =	{{Securing Dynamic Data: A Primer on Differentially Private Data Structures}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.2},
  URN =		{urn:nbn:de:0030-drops-244702},
  doi =		{10.4230/LIPIcs.ESA.2025.2},
  annote =	{Keywords: Differential privacy, continual observation}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.40
Sublinear Space Graph Algorithms in the Continual Release Model

Authors: Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
The graph continual release model of differential privacy seeks to produce differentially private solutions to graph problems under a stream of edge updates where new private solutions are released after each update. Thus far, previously known edge-differentially private algorithms for most graph problems including densest subgraph and matchings in the continual release setting only output real-value estimates (not vertex subset solutions) and do not use sublinear space. Instead, they rely on computing exact graph statistics on the input [Hendrik Fichtenberger et al., 2021; Shuang Song et al., 2018]. In this paper, we leverage sparsification to address the above shortcomings for edge-insertion streams. Our edge-differentially private algorithms use sublinear space with respect to the number of edges in the graph while some also achieve sublinear space in the number of vertices in the graph. In addition, for the densest subgraph problem, we also output edge-differentially private vertex subset solutions; no previous graph algorithms in the continual release model output such subsets. We make novel use of assorted sparsification techniques from the non-private streaming and static graph algorithms literature to achieve new results in the sublinear space, continual release setting. This includes algorithms for densest subgraph, maximum matching, as well as the first continual release k-core decomposition algorithm. We also develop a novel sparse level data structure for k-core decomposition that may be of independent interest. To complement our insertion-only algorithms, we conclude with polynomial additive error lower bounds for edge-privacy in the fully dynamic setting, where only logarithmic lower bounds were previously known.
Cite as

Alessandro Epasto, Quanquan C. Liu, Tamalika Mukherjee, and Felix Zhou. Sublinear Space Graph Algorithms in the Continual Release Model. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 40:1-40:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{epasto_et_al:LIPIcs.APPROX/RANDOM.2025.40,
  author =	{Epasto, Alessandro and Liu, Quanquan C. and Mukherjee, Tamalika and Zhou, Felix},
  title =	{{Sublinear Space Graph Algorithms in the Continual Release Model}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{40:1--40:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.40},
  URN =		{urn:nbn:de:0030-drops-244064},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.40},
  annote =	{Keywords: Differential Privacy, Continual Release, Densest Subgraph, k-Core Decomposition, Maximum Matching}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.65
Solving Linear Programs with Differential Privacy

Authors: Alina Ene, Huy Le Nguyen, Ta Duy Nguyen, and Adrian Vladu

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We study the problem of solving linear programs of the form Ax ≤ b, x ≥ 0 with differential privacy. For homogeneous LPs Ax ≥ 0, we give an efficient (ε,δ)-differentially private algorithm which with probability at least 1-β finds in polynomial time a solution that satisfies all but O(d²/ε log²(d/(δβ))√{log 1/ρ₀}) constraints, for problems with margin ρ₀ > 0. This improves the bound of O(d⁵/ε log^{1.5} 1/ρ₀ polylog(d,1/δ,1/β)) by [Kaplan-Mansour-Moran-Stemmer-Tur, STOC '25]. For general LPs Ax ≤ b, x ≥ 0 with potentially zero margin, we give an efficient (ε,δ)-differentially private algorithm that w.h.p drops O(d⁴/ε log^{2.5} d/δ √{log dU}) constraints, where U is an upper bound for the entries of A and b in absolute value. This improves the result by Kaplan et al. by at least a factor of d⁵. Our techniques build upon privatizing a rescaling perceptron algorithm by [Hoberg-Rothvoss, IPCO '17] and a more refined iterative procedure for identifying equality constraints by Kaplan et al.
Cite as

Alina Ene, Huy Le Nguyen, Ta Duy Nguyen, and Adrian Vladu. Solving Linear Programs with Differential Privacy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 65:1-65:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ene_et_al:LIPIcs.APPROX/RANDOM.2025.65,
  author =	{Ene, Alina and Le Nguyen, Huy and Nguyen, Ta Duy and Vladu, Adrian},
  title =	{{Solving Linear Programs with Differential Privacy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{65:1--65:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.65},
  URN =		{urn:nbn:de:0030-drops-244315},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.65},
  annote =	{Keywords: Differential Privacy, Linear Programming}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.48
Differentially Private Continual Releases of Streaming Frequency Moment Estimations

Authors: Alessandro Epasto, Jieming Mao, Andres Munoz Medina, Vahab Mirrokni, Sergei Vassilvitskii, and Peilin Zhong

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

Abstract
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.
Cite as

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}
}
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