DROPS

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DOI: 10.4230/LIPIcs.FORC.2026.1

Computational Hardness of Private Coreset

Authors: Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, and Pasin Manurangsi

Published in: LIPIcs, Volume 368, 7th Symposium on Foundations of Responsible Computing (FORC 2026)

Abstract

We study the problem of differentially private (DP) computation of coreset for the k-means objective. For a given input set of points, a coreset is another set of points such that the k-means objective for any candidate solution is preserved up to a multiplicative (1 ± α) factor (and some additive factor). We prove the first computational lower bounds for this problem. Specifically, assuming the existence of one-way functions, we show that no polynomial-time (ε, 1/n^{ω(1)})-DP algorithm can compute a coreset for k-means in the 𝓁_∞-metric for some constant α > 0 (and some constant additive factor), even for k = 3. For k-means in the Euclidean metric, we show a similar result but only for α = Θ(1/d²), where d is the dimension.

Cite as

Badih Ghazi, Cristóbal Guzmán, Pritish Kamath, Alexander Knop, Ravi Kumar, and Pasin Manurangsi. Computational Hardness of Private Coreset. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{ghazi_et_al:LIPIcs.FORC.2026.1,
  author =	{Ghazi, Badih and Guzm\'{a}n, Crist\'{o}bal and Kamath, Pritish and Knop, Alexander and Kumar, Ravi and Manurangsi, Pasin},
  title =	{{Computational Hardness of Private Coreset}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{1:1--1:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-419-2},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{368},
  editor =	{Lin, Huijia (Rachel)},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2026.1},
  URN =		{urn:nbn:de:0030-drops-259725},
  doi =		{10.4230/LIPIcs.FORC.2026.1},
  annote =	{Keywords: Differentially Private Clustering, Coreset, Cryptographic Hardness}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.104

Dimension-Free Correlated Sampling for the Hypersimplex

Authors: Joseph (Seffi) Naor, Nitya Raju, Abhishek Shetty, Aravind Srinivasan, Renata Valieva, and David Wajc

Published in: LIPIcs, Volume 362, 17th Innovations in Theoretical Computer Science Conference (ITCS 2026)

Abstract

Sampling from multiple distributions so as to maximize overlap has been studied by statisticians since the 1950s. Since the 2000s, such correlated sampling from the probability simplex has been a powerful building block in disparate areas of theoretical computer science. We study a generalization of this problem to sampling sets from given vectors in the hypersimplex, i.e., outputting sets of size (at most) k ∈ [n], while maximizing the overlap of the sampled sets. Specifically, the expected difference between two output sets should be at most α times their input vectors' 𝓁₁ distance. A value of α = O(log n) is known to be achievable, due to Chen et al. (ICALP'17). We improve this factor to O(log k), independent of the ambient dimension n. Our algorithm satisfies other desirable properties, including (up to a log^* n factor) input-sparsity sampling time, logarithmic parallel depth and dynamic update time, as well as preservation of submodular objectives. Anticipating broader use of correlated sampling algorithms for the hypersimplex, we present applications of our algorithm to online paging, offline approximation of metric multi-labeling, and swift multi-scenario submodular welfare approximating reallocation.

Cite as

Joseph (Seffi) Naor, Nitya Raju, Abhishek Shetty, Aravind Srinivasan, Renata Valieva, and David Wajc. Dimension-Free Correlated Sampling for the Hypersimplex. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 104:1-104:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{naor_et_al:LIPIcs.ITCS.2026.104,
  author =	{Naor, Joseph (Seffi) and Raju, Nitya and Shetty, Abhishek and Srinivasan, Aravind and Valieva, Renata and Wajc, David},
  title =	{{Dimension-Free Correlated Sampling for the Hypersimplex}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{104:1--104:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-410-9},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{362},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2026.104},
  URN =		{urn:nbn:de:0030-drops-253918},
  doi =		{10.4230/LIPIcs.ITCS.2026.104},
  annote =	{Keywords: Correlated Rounding, Dependent Rounding}
}

Document

DOI: 10.4230/LIPIcs.FORC.2025.12

Infinitely Divisible Noise for Differential Privacy: Nearly Optimal Error in the High ε Regime

Authors: Charlie Harrison and Pasin Manurangsi

Published in: LIPIcs, Volume 329, 6th Symposium on Foundations of Responsible Computing (FORC 2025)

Abstract

Differential privacy (DP) can be achieved in a distributed manner, where multiple parties add independent noise such that their sum protects the overall dataset with DP. A common technique here is for each party to sample their noise from the decomposition of an infinitely divisible distribution. We analyze two mechanisms in this setting: 1) the generalized discrete Laplace (GDL) mechanism, whose distribution (which is closed under summation) follows from differences of i.i.d. negative binomial shares, and 2) the multi-scale discrete Laplace (MSDLap) mechanism, a novel mechanism following the sum of multiple i.i.d. discrete Laplace shares at different scales. For ε ≥ 1, our mechanisms can be parameterized to have O(Δ³ e^{-ε}) and O(min(Δ³ e^{-ε}, Δ² e^{-2ε/3})) MSE, respectively, where Δ denote the sensitivity; the latter bound matches known optimality results. Furthermore, the MSDLap mechanism has the optimal MSE including constants as ε → ∞. We also show a transformation from the discrete setting to the continuous setting, which allows us to transform both mechanisms to the continuous setting and thereby achieve the optimal O(Δ² e^{-2ε / 3}) MSE. To our knowledge, these are the first infinitely divisible additive noise mechanisms that achieve order-optimal MSE under pure DP for either the discrete or continuous setting, so our work shows formally there is no separation in utility when query-independent noise adding mechanisms are restricted to infinitely divisible noise. For the continuous setting, our result improves upon Pagh and Stausholm’s Arete distribution which gives an MSE of O(Δ² e^{-ε/4}) [Pagh and Stausholm, 2022]. Furthermore, we give an exact sampler tuned to efficiently implement the MSDLap mechanism, and we apply our results to improve a state of the art multi-message shuffle DP protocol from [Balle et al., 2020] in the high ε regime.

Cite as

Charlie Harrison and Pasin Manurangsi. Infinitely Divisible Noise for Differential Privacy: Nearly Optimal Error in the High ε Regime. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 12:1-12:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{harrison_et_al:LIPIcs.FORC.2025.12,
  author =	{Harrison, Charlie and Manurangsi, Pasin},
  title =	{{Infinitely Divisible Noise for Differential Privacy: Nearly Optimal Error in the High \epsilon Regime}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{12:1--12:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-367-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{329},
  editor =	{Bun, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2025.12},
  URN =		{urn:nbn:de:0030-drops-231396},
  doi =		{10.4230/LIPIcs.FORC.2025.12},
  annote =	{Keywords: Differential Privacy, Distributed Noise Addition}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.13

Low Sensitivity Hopsets

Authors: Vikrant Ashvinkumar, Aaron Bernstein, Chengyuan Deng, Jie Gao, and Nicole Wein

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

Given a weighted graph G = (V,E,w), a (β, ε)-hopset H is an edge set such that for any s,t ∈ V, where s can reach t in G, there is a path from s to t in G ∪ H which uses at most β hops whose length is in the range [dist_G(s,t), (1+ε)dist_G(s,t)]. We break away from the traditional question that asks for a hopset H that achieves small |H| and small diameter β and instead study the sensitivity of H, a new quality measure. The sensitivity of a vertex (or edge) given a hopset H is, informally, the number of times a single hop in G ∪ H bypasses it; a bit more formally, assuming shortest paths in G are unique, it is the number of hopset edges (s,t) ∈ H such that the vertex (or edge) is contained in the unique st-path in G having length exactly dist_G(s,t). The sensitivity associated with H is then the maximum sensitivity over all vertices (or edges). The highlights of our results are: - A construction for (Õ(√n), 0)-hopsets on undirected graphs with O(log n) sensitivity, complemented with a lower bound showing that Õ(√n) is tight up to polylogarithmic factors for any construction with polylogarithmic sensitivity. - A construction for (n^o(1), ε)-hopsets on undirected graphs with n^o(1) sensitivity for any ε > 0 that is at least inverse polylogarithmic, complemented with a lower bound on the tradeoff between β, ε, and the sensitivity. - We define a notion of sensitivity for β-shortcut sets (which are the reachability analogues of hopsets) and give a construction for Õ(√n)-shortcut sets on directed graphs with O(log n) sensitivity, complemented with a lower bound showing that β = Ω̃(n^{1/3}) for any construction with polylogarithmic sensitivity. We believe hopset sensitivity is a natural measure in and of itself, and could potentially find use in a diverse range of contexts. More concretely, the notion of hopset sensitivity is also directly motivated by the Differentially Private All Sets Range Queries problem [Deng et al. WADS 23]. Our result for O(log n) sensitivity (Õ(√n), 0)-hopsets on undirected graphs immediately improves the current best-known upper bound on utility from Õ(n^{1/3}) to Õ(n^{1/4}) in the pure-DP setting, which is tight up to polylogarithmic factors.

Cite as

Vikrant Ashvinkumar, Aaron Bernstein, Chengyuan Deng, Jie Gao, and Nicole Wein. Low Sensitivity Hopsets. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ashvinkumar_et_al:LIPIcs.ITCS.2025.13,
  author =	{Ashvinkumar, Vikrant and Bernstein, Aaron and Deng, Chengyuan and Gao, Jie and Wein, Nicole},
  title =	{{Low Sensitivity Hopsets}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.13},
  URN =		{urn:nbn:de:0030-drops-226418},
  doi =		{10.4230/LIPIcs.ITCS.2025.13},
  annote =	{Keywords: Hopsets, Shortcuts, Sensitivity, Differential Privacy}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.25

Locally Private Histograms in All Privacy Regimes

Authors: Clément L. Canonne and Abigail Gentle

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

Frequency estimation, a.k.a. histograms, is a workhorse of data analysis, and as such has been thoroughly studied under differentially privacy. In particular, computing histograms in the local model of privacy has been the focus of a fruitful recent line of work, and various algorithms have been proposed, achieving the order-optimal 𝓁_∞ error in the high-privacy (small ε) regime while balancing other considerations such as time- and communication-efficiency. However, to the best of our knowledge, the picture is much less clear when it comes to the medium- or low-privacy regime (large ε), despite its increased relevance in practice. In this paper, we investigate locally private histograms, and the very related distribution learning task, in this medium-to-low privacy regime, and establish near-tight (and somewhat unexpected) bounds on the 𝓁_∞ error achievable. As a direct corollary of our results, we obtain a protocol for histograms in the shuffle model of differential privacy, with accuracy matching previous algorithms but significantly better message and communication complexity. Our theoretical findings emerge from a novel analysis, which appears to improve bounds across the board for the locally private histogram problem. We back our theoretical findings by an empirical comparison of existing algorithms in all privacy regimes, to assess their typical performance and behaviour beyond the worst-case setting.

Cite as

Clément L. Canonne and Abigail Gentle. Locally Private Histograms in All Privacy Regimes. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 25:1-25:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{canonne_et_al:LIPIcs.ITCS.2025.25,
  author =	{Canonne, Cl\'{e}ment L. and Gentle, Abigail},
  title =	{{Locally Private Histograms in All Privacy Regimes}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{25:1--25:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.25},
  URN =		{urn:nbn:de:0030-drops-226532},
  doi =		{10.4230/LIPIcs.ITCS.2025.25},
  annote =	{Keywords: Differential Privacy, Local Differential Privacy, Histograms, Frequency Estimation, Lower Bounds, Maximum Error}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.27

The Randomness Complexity of Differential Privacy

Authors: Clément L. Canonne, Francis E. Su, and Salil P. Vadhan

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

We initiate the study of the randomness complexity of differential privacy, i.e., how many random bits an algorithm needs in order to generate accurate differentially private releases. As a test case, we focus on the task of releasing the results of d counting queries, or equivalently all one-way marginals on a d-dimensional dataset with boolean attributes. While standard differentially private mechanisms for this task have randomness complexity that grows linearly with d, we show that, surprisingly, only log₂ d+O(1) random bits (in expectation) suffice to achieve an error that depends polynomially on d (and is independent of the size n of the dataset), and furthermore this is possible with pure, unbounded differential privacy and privacy-loss parameter ε = 1/poly(d). Conversely, we show that at least log₂ d-O(1) random bits are also necessary for nontrivial accuracy, even with approximate, bounded DP, provided the privacy-loss parameters satisfy ε,δ ≤ 1/poly(d). We obtain our results by establishing a close connection between the randomness complexity of differentially private mechanisms and the geometric notion of "deterministic rounding schemes" recently introduced and studied by Vander Woude et al. (2022, 2023).

Cite as

Clément L. Canonne, Francis E. Su, and Salil P. Vadhan. The Randomness Complexity of Differential Privacy. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 27:1-27:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{canonne_et_al:LIPIcs.ITCS.2025.27,
  author =	{Canonne, Cl\'{e}ment L. and Su, Francis E. and Vadhan, Salil P.},
  title =	{{The Randomness Complexity of Differential Privacy}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{27:1--27:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.27},
  URN =		{urn:nbn:de:0030-drops-226556},
  doi =		{10.4230/LIPIcs.ITCS.2025.27},
  annote =	{Keywords: differential privacy, randomness, geometry}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2025.53

Differential Privacy on Trust Graphs

Authors: Badih Ghazi, Ravi Kumar, Pasin Manurangsi, and Serena Wang

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract

We study differential privacy (DP) in a multi-party setting where each party only trusts a (known) subset of the other parties with its data. Specifically, given a trust graph where vertices correspond to parties and neighbors are mutually trusting, we give a DP algorithm for aggregation with a much better privacy-utility trade-off than in the well-studied local model of DP (where each party trusts no other party). We further study a robust variant where each party trusts all but an unknown subset of at most t of its neighbors (where t is a given parameter), and give an algorithm for this setting. We complement our algorithms with lower bounds, and discuss implications of our work to other tasks in private learning and analytics.

Cite as

Badih Ghazi, Ravi Kumar, Pasin Manurangsi, and Serena Wang. Differential Privacy on Trust Graphs. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 53:1-53:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{ghazi_et_al:LIPIcs.ITCS.2025.53,
  author =	{Ghazi, Badih and Kumar, Ravi and Manurangsi, Pasin and Wang, Serena},
  title =	{{Differential Privacy on Trust Graphs}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{53:1--53:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.53},
  URN =		{urn:nbn:de:0030-drops-226816},
  doi =		{10.4230/LIPIcs.ITCS.2025.53},
  annote =	{Keywords: Differential privacy, trust graphs, minimum dominating set, packing number}
}

Document

DOI: 10.4230/LIPIcs.ITC.2024.4

Pure-DP Aggregation in the Shuffle Model: Error-Optimal and Communication-Efficient

Authors: Badih Ghazi, Ravi Kumar, and Pasin Manurangsi

Published in: LIPIcs, Volume 304, 5th Conference on Information-Theoretic Cryptography (ITC 2024)

Abstract

We obtain a new protocol for binary counting in the ε-DP_shuffle model with error O(1/ε) and expected communication Õ((log n)/ε) messages per user. Previous protocols incur either an error of O(1/ε^1.5) with O_ε(log n) messages per user (Ghazi et al., ITC 2020) or an error of O(1/ε) with O_ε(n²) messages per user (Cheu and Yan, TPDP 2022). Using the new protocol, we obtained improved ε-DP_shuffle protocols for real summation and histograms.

Cite as

Badih Ghazi, Ravi Kumar, and Pasin Manurangsi. Pure-DP Aggregation in the Shuffle Model: Error-Optimal and Communication-Efficient. In 5th Conference on Information-Theoretic Cryptography (ITC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 304, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ghazi_et_al:LIPIcs.ITC.2024.4,
  author =	{Ghazi, Badih and Kumar, Ravi and Manurangsi, Pasin},
  title =	{{Pure-DP Aggregation in the Shuffle Model: Error-Optimal and Communication-Efficient}},
  booktitle =	{5th Conference on Information-Theoretic Cryptography (ITC 2024)},
  pages =	{4:1--4:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-333-1},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{304},
  editor =	{Aggarwal, Divesh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2024.4},
  URN =		{urn:nbn:de:0030-drops-205127},
  doi =		{10.4230/LIPIcs.ITC.2024.4},
  annote =	{Keywords: Differential Privacy, Shuffle Model, Aggregation, Pure Differential Privacy}
}

Document

DOI: 10.4230/LIPIcs.ITC.2023.17

Differentially Private Aggregation via Imperfect Shuffling

Authors: Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Jelani Nelson, and Samson Zhou

Published in: LIPIcs, Volume 267, 4th Conference on Information-Theoretic Cryptography (ITC 2023)

Abstract

In this paper, we introduce the imperfect shuffle differential privacy model, where messages sent from users are shuffled in an almost uniform manner before being observed by a curator for private aggregation. We then consider the private summation problem. We show that the standard split-and-mix protocol by Ishai et. al. [FOCS 2006] can be adapted to achieve near-optimal utility bounds in the imperfect shuffle model. Specifically, we show that surprisingly, there is no additional error overhead necessary in the imperfect shuffle model.

Cite as

Badih Ghazi, Ravi Kumar, Pasin Manurangsi, Jelani Nelson, and Samson Zhou. Differentially Private Aggregation via Imperfect Shuffling. In 4th Conference on Information-Theoretic Cryptography (ITC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 267, pp. 17:1-17:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ghazi_et_al:LIPIcs.ITC.2023.17,
  author =	{Ghazi, Badih and Kumar, Ravi and Manurangsi, Pasin and Nelson, Jelani and Zhou, Samson},
  title =	{{Differentially Private Aggregation via Imperfect Shuffling}},
  booktitle =	{4th Conference on Information-Theoretic Cryptography (ITC 2023)},
  pages =	{17:1--17:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-271-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{267},
  editor =	{Chung, Kai-Min},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.17},
  URN =		{urn:nbn:de:0030-drops-183453},
  doi =		{10.4230/LIPIcs.ITC.2023.17},
  annote =	{Keywords: Differential privacy, private summation, shuffle model}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.66

On Differentially Private Counting on Trees

Authors: Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, and Kewen Wu

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

We study the problem of performing counting queries at different levels in hierarchical structures while preserving individuals' privacy. Motivated by applications, we propose a new error measure for this problem by considering a combination of multiplicative and additive approximation to the query results. We examine known mechanisms in differential privacy (DP) and prove their optimality, under this measure, in the pure-DP setting. In the approximate-DP setting, we design new algorithms achieving significant improvements over known ones.

Cite as

Badih Ghazi, Pritish Kamath, Ravi Kumar, Pasin Manurangsi, and Kewen Wu. On Differentially Private Counting on Trees. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 66:1-66:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ghazi_et_al:LIPIcs.ICALP.2023.66,
  author =	{Ghazi, Badih and Kamath, Pritish and Kumar, Ravi and Manurangsi, Pasin and Wu, Kewen},
  title =	{{On Differentially Private Counting on Trees}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{66:1--66:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.66},
  URN =		{urn:nbn:de:0030-drops-181186},
  doi =		{10.4230/LIPIcs.ICALP.2023.66},
  annote =	{Keywords: Differential Privacy, Algorithms, Trees, Hierarchies}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2023.97

Decidability of Fully Quantum Nonlocal Games with Noisy Maximally Entangled States

Authors: Minglong Qin and Penghui Yao

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract

This paper considers the decidability of fully quantum nonlocal games with noisy maximally entangled states. Fully quantum nonlocal games are a generalization of nonlocal games, where both questions and answers are quantum and the referee performs a binary POVM measurement to decide whether they win the game after receiving the quantum answers from the players. The quantum value of a fully quantum nonlocal game is the supremum of the probability that they win the game, where the supremum is taken over all the possible entangled states shared between the players and all the valid quantum operations performed by the players. The seminal work MIP^* = RE [Zhengfeng Ji et al., 2020; Zhengfeng Ji et al., 2020] implies that it is undecidable to approximate the quantum value of a fully nonlocal game. This still holds even if the players are only allowed to share (arbitrarily many copies of) maximally entangled states. This paper investigates the case that the shared maximally entangled states are noisy. We prove that there is a computable upper bound on the copies of noisy maximally entangled states for the players to win a fully quantum nonlocal game with a probability arbitrarily close to the quantum value. This implies that it is decidable to approximate the quantum values of these games. Hence, the hardness of approximating the quantum value of a fully quantum nonlocal game is not robust against the noise in the shared states. This paper is built on the framework for the decidability of non-interactive simulations of joint distributions [Badih Ghazi et al., 2016; De et al., 2018; Ghazi et al., 2018] and generalizes the analogous result for nonlocal games in [Qin and Yao, 2021]. We extend the theory of Fourier analysis to the space of super-operators and prove several key results including an invariance principle and a dimension reduction for super-operators. These results are interesting in their own right and are believed to have further applications.

Cite as

Minglong Qin and Penghui Yao. Decidability of Fully Quantum Nonlocal Games with Noisy Maximally Entangled States. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 97:1-97:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{qin_et_al:LIPIcs.ICALP.2023.97,
  author =	{Qin, Minglong and Yao, Penghui},
  title =	{{Decidability of Fully Quantum Nonlocal Games with Noisy Maximally Entangled States}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{97:1--97:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.97},
  URN =		{urn:nbn:de:0030-drops-181499},
  doi =		{10.4230/LIPIcs.ICALP.2023.97},
  annote =	{Keywords: Fully quantum nonlocal games, Fourier analysis, Dimension reduction}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2023.54

Algorithms with More Granular Differential Privacy Guarantees

Authors: Badih Ghazi, Ravi Kumar, Pasin Manurangsi, and Thomas Steinke

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

Abstract

Differential privacy is often applied with a privacy parameter that is larger than the theory suggests is ideal; various informal justifications for tolerating large privacy parameters have been proposed. In this work, we consider partial differential privacy (DP), which allows quantifying the privacy guarantee on a per-attribute basis. We study several basic data analysis and learning tasks in this framework, and design algorithms whose per-attribute privacy parameter is smaller that the best possible privacy parameter for the entire record of a person (i.e., all the attributes).

Cite as

Badih Ghazi, Ravi Kumar, Pasin Manurangsi, and Thomas Steinke. Algorithms with More Granular Differential Privacy Guarantees. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 54:1-54:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ghazi_et_al:LIPIcs.ITCS.2023.54,
  author =	{Ghazi, Badih and Kumar, Ravi and Manurangsi, Pasin and Steinke, Thomas},
  title =	{{Algorithms with More Granular Differential Privacy Guarantees}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{54:1--54:24},
  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.2023.54},
  URN =		{urn:nbn:de:0030-drops-175574},
  doi =		{10.4230/LIPIcs.ITCS.2023.54},
  annote =	{Keywords: Differential Privacy, Algorithms, Per-Attribute Privacy}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2023.55

Private Counting of Distinct and k-Occurring Items in Time Windows

Authors: Badih Ghazi, Ravi Kumar, Jelani Nelson, and Pasin Manurangsi

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

Abstract

In this work, we study the task of estimating the numbers of distinct and k-occurring items in a time window under the constraint of differential privacy (DP). We consider several variants depending on whether the queries are on general time windows (between times t₁ and t₂), or are restricted to being cumulative (between times 1 and t₂), and depending on whether the DP neighboring relation is event-level or the more stringent item-level. We obtain nearly tight upper and lower bounds on the errors of DP algorithms for these problems. En route, we obtain an event-level DP algorithm for estimating, at each time step, the number of distinct items seen over the last W updates with error polylogarithmic in W; this answers an open question of Bolot et al. (ICDT 2013).

Cite as

Badih Ghazi, Ravi Kumar, Jelani Nelson, and Pasin Manurangsi. Private Counting of Distinct and k-Occurring Items in Time Windows. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 55:1-55:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{ghazi_et_al:LIPIcs.ITCS.2023.55,
  author =	{Ghazi, Badih and Kumar, Ravi and Nelson, Jelani and Manurangsi, Pasin},
  title =	{{Private Counting of Distinct and k-Occurring Items in Time Windows}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{55:1--55:24},
  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.2023.55},
  URN =		{urn:nbn:de:0030-drops-175580},
  doi =		{10.4230/LIPIcs.ITCS.2023.55},
  annote =	{Keywords: Differential Privacy, Algorithms, Distinct Elements, Time Windows}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.7

Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems

Authors: Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, and Pasin Manurangsi

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract

We study several questions related to diversifying search results. We give improved approximation algorithms in each of the following problems, together with some lower bounds. 1) We give a polynomial-time approximation scheme (PTAS) for a diversified search ranking problem [Nikhil Bansal et al., 2010] whose objective is to minimizes the discounted cumulative gain. Our PTAS runs in time n^{2^O(log(1/ε)/ε)} ⋅ m^O(1) where n denotes the number of elements in the databases and m denotes the number of constraints. Complementing this result, we show that no PTAS can run in time f(ε) ⋅ (nm)^{2^o(1/ε)} assuming Gap-ETH and therefore our running time is nearly tight. Both our upper and lower bounds answer open questions from [Nikhil Bansal et al., 2010]. 2) We next consider the Max-Sum Dispersion problem, whose objective is to select k out of n elements from a database that maximizes the dispersion, which is defined as the sum of the pairwise distances under a given metric. We give a quasipolynomial-time approximation scheme (QPTAS) for the problem which runs in time n^{O_ε(log n)}. This improves upon previously known polynomial-time algorithms with approximate ratios 0.5 [Refael Hassin et al., 1997; Allan Borodin et al., 2017]. Furthermore, we observe that reductions from previous work rule out approximation schemes that run in n^õ_ε(log n) time assuming ETH. 3) Finally, we consider a generalization of Max-Sum Dispersion called Max-Sum Diversification. In addition to the sum of pairwise distance, the objective also includes another function f. For monotone submodular function f, we give a quasipolynomial-time algorithm with approximation ratio arbitrarily close to (1-1/e). This improves upon the best polynomial-time algorithm which has approximation ratio 0.5 [Allan Borodin et al., 2017]. Furthermore, the (1-1/e) factor is also tight as achieving better-than-(1-1/e) approximation is NP-hard [Uriel Feige, 1998].

Cite as

Amir Abboud, Vincent Cohen-Addad, Euiwoong Lee, and Pasin Manurangsi. Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 7:1-7:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{abboud_et_al:LIPIcs.ICALP.2022.7,
  author =	{Abboud, Amir and Cohen-Addad, Vincent and Lee, Euiwoong and Manurangsi, Pasin},
  title =	{{Improved Approximation Algorithms and Lower Bounds for Search-Diversification Problems}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{7:1--7:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.7},
  URN =		{urn:nbn:de:0030-drops-163481},
  doi =		{10.4230/LIPIcs.ICALP.2022.7},
  annote =	{Keywords: Approximation Algorithms, Complexity, Data Mining, Diversification}
}

Document

Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.55

High-Probability List-Recovery, and Applications to Heavy Hitters

Authors: Dean Doron and Mary Wootters

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract

An error correcting code 𝒞 : Σ^k → Σⁿ is efficiently list-recoverable from input list size 𝓁 if for any sets ℒ₁, …, ℒ_n ⊆ Σ of size at most 𝓁, one can efficiently recover the list ℒ = {x ∈ Σ^k : ∀ j ∈ [n], 𝒞(x)_j ∈ ℒ_j}. While list-recovery has been well-studied in error correcting codes, all known constructions with "efficient" algorithms are not efficient in the parameter 𝓁. In this work, motivated by applications in algorithm design and pseudorandomness, we study list-recovery with the goal of obtaining a good dependence on 𝓁. We make a step towards this goal by obtaining it in the weaker case where we allow a randomized encoding map and a small failure probability, and where the input lists are derived from unions of codewords. As an application of our construction, we give a data structure for the heavy hitters problem in the strict turnstile model that, for some parameter regimes, obtains stronger guarantees than known constructions.

Cite as

Dean Doron and Mary Wootters. High-Probability List-Recovery, and Applications to Heavy Hitters. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{doron_et_al:LIPIcs.ICALP.2022.55,
  author =	{Doron, Dean and Wootters, Mary},
  title =	{{High-Probability List-Recovery, and Applications to Heavy Hitters}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{55:1--55:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.55},
  URN =		{urn:nbn:de:0030-drops-163961},
  doi =		{10.4230/LIPIcs.ICALP.2022.55},
  annote =	{Keywords: List recoverable codes, Heavy Hitters, high-dimensional expanders}
}

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