29 Search Results for "McSherry, Frank"

Document
DOI: 10.4230/LIPIcs.STACS.2026.71
Broadcast in Almost Mixing Time

Authors: Anton Paramonov and Roger Wattenhofer

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We study the problem of broadcasting multiple messages in the CONGEST model. In this problem, a dedicated source node s possesses a set M of messages with every message of size O(log n) where n is the total number of nodes. The objective is to ensure that every node in the network learns all messages in M. The execution of an algorithm progresses in rounds, and we focus on optimizing the round complexity of broadcasting multiple messages. Our primary contribution is a randomized algorithm for networks with expander topology. The algorithm succeeds with high probability and achieves a round complexity that is optimal up to a factor of the network’s mixing time and polylogarithmic terms. It leverages a multi-COBRA primitive, which uses multiple branching random walks running in parallel. A crucial aspect of our method is the use of these branching random walks to construct an optimal (up to a polylogarithmic factor) tree packing of a random graph, which is then used for efficient broadcasting. We also prove the problem to be NP-hard in a centralized setting and provide insights into why lower bounds that can be matched in expanders, namely graph diameter and |M|/minCut, cannot be tight in general graphs.
Cite as

Anton Paramonov and Roger Wattenhofer. Broadcast in Almost Mixing Time. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 71:1-71:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{paramonov_et_al:LIPIcs.STACS.2026.71,
  author =	{Paramonov, Anton and Wattenhofer, Roger},
  title =	{{Broadcast in Almost Mixing Time}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{71:1--71:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.71},
  URN =		{urn:nbn:de:0030-drops-255603},
  doi =		{10.4230/LIPIcs.STACS.2026.71},
  annote =	{Keywords: Distributed algorithms, Expander Graphs, Random graphs, Broadcast, Branching random walks, Tree packing, CONGEST model}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.21
Differential Privacy from Axioms

Authors: Guy Blanc, William Pires, and Toniann Pitassi

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

Abstract
Differential privacy (DP) is the de facto notion of privacy both in theory and in practice. However, despite its popularity, DP imposes strict requirements which guard against strong worst-case scenarios. For example, it guards against seemingly unrealistic scenarios where an attacker has full information about all but one point in the data set, and still nothing can be learned about the remaining point. While preventing such a strong attack is desirable, many works have explored whether average-case relaxations of DP are easier to satisfy [Hall et al., 2013; Wang et al., 2016; Bassily and Freund, 2016; Liu et al., 2023]. In this work, we are motivated by the question of whether alternate, weaker notions of privacy are possible: can a weakened privacy notion still guarantee some basic level of privacy, and on the other hand, achieve privacy more efficiently and/or for a substantially broader set of tasks? Our main result shows the answer is no: even in the statistical setting, any reasonable measure of privacy satisfying nontrivial composition is equivalent to DP. To prove this, we identify a core set of four axioms or desiderata: pre-processing invariance, prohibition of blatant non-privacy, strong composition, and linear scalability. Our main theorem shows that any privacy measure satisfying our axioms is equivalent to DP, up to polynomial factors in sample complexity. We complement this result by showing our axioms are minimal: removing any one of our axioms enables ill-behaved measures of privacy.
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Guy Blanc, William Pires, and Toniann Pitassi. Differential Privacy from Axioms. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 21:1-21:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blanc_et_al:LIPIcs.ITCS.2026.21,
  author =	{Blanc, Guy and Pires, William and Pitassi, Toniann},
  title =	{{Differential Privacy from Axioms}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{21:1--21:13},
  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.2026.21},
  URN =		{urn:nbn:de:0030-drops-253081},
  doi =		{10.4230/LIPIcs.ITCS.2026.21},
  annote =	{Keywords: Differential Privacy, Privacy Amplification, Composition}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.33
Uniformity Testing Under User-Level Local Privacy

Authors: Clément L. Canonne, Abigail Gentle, and Vikrant Singhal

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

Abstract
We initiate the study of distribution testing under user-level local differential privacy, where each of n users contributes m samples from the unknown underlying distribution. This setting, albeit very natural, is significantly more challenging than the usual locally private setting, as for the same parameter ε the privacy guarantee must now apply to a full batch of m data points. While some recent work considers distribution learning in this user-level setting, nothing was known for even the most fundamental testing task, uniformity testing (and its generalization, identity testing). We address this gap, by providing (nearly) sample-optimal user-level LDP algorithms for uniformity and identity testing. Motivated by practical considerations, our main focus is on the private-coin, symmetric setting, which does not require users to share a common random seed nor to have been assigned a globally unique identifier.
Cite as

Clément L. Canonne, Abigail Gentle, and Vikrant Singhal. Uniformity Testing Under User-Level Local Privacy. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 33:1-33:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{canonne_et_al:LIPIcs.ITCS.2026.33,
  author =	{Canonne, Cl\'{e}ment L. and Gentle, Abigail and Singhal, Vikrant},
  title =	{{Uniformity Testing Under User-Level Local Privacy}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{33:1--33:24},
  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.2026.33},
  URN =		{urn:nbn:de:0030-drops-253201},
  doi =		{10.4230/LIPIcs.ITCS.2026.33},
  annote =	{Keywords: Differential Privacy, Local Differential Privacy, Uniformity Testing, Identity Testing, Hypothesis Testing, User-Level Differential Privacy, Person-Level Differential Privacy}
}
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
DOI: 10.4230/LIPIcs.ESA.2025.91
Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism

Authors: Laxman Dhulipala, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu

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

Abstract
Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the k-core decomposition problem, the classic peeling algorithm iteratively removes a vertex if its induced degree falls below a threshold. The sparse vector technique (SVT) is generally used to transform non-private threshold queries into private ones with only a small additive loss in accuracy. However, a naive application of SVT in the graph setting leads to an amplification of the error by a factor of n due to composition, as SVT is applied to every vertex. In this paper, we resolve this problem by formulating a novel generalized sparse vector technique which we call the Multidimensional AboveThreshold (MAT) Mechanism which generalizes SVT (applied to vectors with one dimension) to vectors with multiple dimensions. When applied to vectors with n dimensions, we solve a number of important graph problems with better bounds than previous work. Specifically, we apply our MAT mechanism to obtain a set of improved bounds for a variety of problems including k-core decomposition, densest subgraph, low out-degree ordering, and vertex coloring. We give a tight local edge differentially private (LEDP) algorithm for k-core decomposition that results in an approximation with O(ε^{-1} log n) additive error and no multiplicative error in O(n) rounds. We also give a new (2+η)-factor multiplicative, O(ε^{-1} log n) additive error algorithm in O(log² n) rounds for any constant η > 0. Both of these results are asymptotically tight against our new lower bound of Ω(log n) for any constant-factor approximation algorithm for k-core decomposition. Our new algorithms for k-core decomposition also directly lead to new algorithms for the related problems of densest subgraph and low out-degree ordering. Finally, we give novel LEDP differentially private defective coloring algorithms that use number of colors given in terms of the arboricity of the graph.
Cite as

Laxman Dhulipala, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu. Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 91:1-91:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dhulipala_et_al:LIPIcs.ESA.2025.91,
  author =	{Dhulipala, Laxman and Henzinger, Monika and Li, George Z. and Liu, Quanquan C. and Sricharan, A. R. and Zhu, Leqi},
  title =	{{Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{91:1--91:20},
  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.2025.91},
  URN =		{urn:nbn:de:0030-drops-245601},
  doi =		{10.4230/LIPIcs.ESA.2025.91},
  annote =	{Keywords: differential privacy, abovethreshold, densest subgraph}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.30
Nondeterministic Asynchronous Dataflow in Isabelle/HOL

Authors: Rafael Castro Gonçalves Silva, Laouen Fernet, and Dmitriy Traytel

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
We formalize nondeterministic asynchronous dataflow networks in Isabelle/HOL. Dataflow networks are comprised of operators that are capable of communicating with the network, performing silent computations, and making nondeterministic choices. We represent operators using a shallow embedding as codatatypes. Using this representation, we define standard asynchronous dataflow primitives, including sequential and parallel composition and a feedback operator. These primitives adhere to a number of laws from the literature, which we prove by coinduction using weak bisimilarity as our equality. Albeit coinductive and nondeterministic, our model is executable via code extraction to Haskell.
Cite as

Rafael Castro Gonçalves Silva, Laouen Fernet, and Dmitriy Traytel. Nondeterministic Asynchronous Dataflow in Isabelle/HOL. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 30:1-30:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{silva_et_al:LIPIcs.ITP.2025.30,
  author =	{Silva, Rafael Castro Gon\c{c}alves and Fernet, Laouen and Traytel, Dmitriy},
  title =	{{Nondeterministic Asynchronous Dataflow in Isabelle/HOL}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{30:1--30:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.30},
  URN =		{urn:nbn:de:0030-drops-246280},
  doi =		{10.4230/LIPIcs.ITP.2025.30},
  annote =	{Keywords: dataflow, verification, coinduction, Isabelle/HOL}
}
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.2025.33
Bit-Fixing Extractors for Almost-Logarithmic Entropy

Authors: Dean Doron and Ori Fridman

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

Abstract
An oblivious bit-fixing source is a distribution over {0,1}ⁿ, where k bits are uniform and independent and the rest n-k are fixed a priori to some constant value. Extracting (close to) true randomness from an oblivious bit-fixing source has been studied since the 1980s, with applications in cryptography and complexity theory. We construct explicit extractors for oblivious bit-fixing source that support k = Õ(log n), outputting almost all the entropy with low error. The previous state-of-the-art construction that outputs many bits is due to Rao [Rao, CCC '09], and requires entropy k ≥ log^{c} n for some large constant c. The two key components in our constructions are new low-error affine condensers for poly-logarithmic entropies (that we achieve using techniques from the nonmalleable extractors literature), and a dual use of linear condensers for OBF sources.
Cite as

Dean Doron and Ori Fridman. Bit-Fixing Extractors for Almost-Logarithmic Entropy. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{doron_et_al:LIPIcs.APPROX/RANDOM.2025.33,
  author =	{Doron, Dean and Fridman, Ori},
  title =	{{Bit-Fixing Extractors for Almost-Logarithmic Entropy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{33:1--33:19},
  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.2025.33},
  URN =		{urn:nbn:de:0030-drops-243994},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.33},
  annote =	{Keywords: Seedless extractors, oblivious bit-fixing sources}
}
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.ECOOP.2025.20
Incremental Computing by Differential Execution

Authors: Prashant Kumar, André Pacak, and Sebastian Erdweg

Published in: LIPIcs, Volume 333, 39th European Conference on Object-Oriented Programming (ECOOP 2025)

Abstract
Incremental computing offers the potential for significant performance gains by efficiently updating computations in response to changing data. However, traditional approaches are either problem-specific or use an inefficient all-or-nothing strategy of rerunning affected computations entirely. This paper presents differential semantics, a novel approach that directly embeds the propagation of changes into the semantics of a general-purpose programming language. Given a precise description of input changes, differential semantics rules define how these changes are tracked and propagated through core language constructs like assignments, conditionals, and loops to produce corresponding output changes. We formalize differential semantics and verify key properties, including correctness, using the Rocq proof assistant. We also develop and formally prove a set of optimizations, particularly for loop handling, that enable asymptotic performance improvements. An implementation of the semantics as a differential interpreter achieves order-of-magnitude speedups over recomputation on the Bellman-Ford shortest path algorithm.
Cite as

Prashant Kumar, André Pacak, and Sebastian Erdweg. Incremental Computing by Differential Execution. In 39th European Conference on Object-Oriented Programming (ECOOP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 333, pp. 20:1-20:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumar_et_al:LIPIcs.ECOOP.2025.20,
  author =	{Kumar, Prashant and Pacak, Andr\'{e} and Erdweg, Sebastian},
  title =	{{Incremental Computing by Differential Execution}},
  booktitle =	{39th European Conference on Object-Oriented Programming (ECOOP 2025)},
  pages =	{20:1--20:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-373-7},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{333},
  editor =	{Aldrich, Jonathan and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2025.20},
  URN =		{urn:nbn:de:0030-drops-233137},
  doi =		{10.4230/LIPIcs.ECOOP.2025.20},
  annote =	{Keywords: Incremental computing, differential semantics, programming language design, formal verification, big-step semantics}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.3
Private Estimation When Data and Privacy Demands Are Correlated

Authors: Syomantak Chaudhuri and Thomas A. Courtade

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

Abstract
Differential Privacy (DP) is the current gold-standard for ensuring privacy for statistical queries. Estimation problems under DP constraints appearing in the literature have largely focused on providing equal privacy to all users. We consider the problems of empirical mean estimation for univariate data and frequency estimation for categorical data, both subject to heterogeneous privacy constraints. Each user, contributing a sample to the dataset, is allowed to have a different privacy demand. The dataset itself is assumed to be worst-case and we study both problems under two different formulations - first, where privacy demands and data may be correlated, and second, where correlations are weakened by random permutation of the dataset. We establish theoretical performance guarantees for our proposed algorithms, under both PAC error and mean-squared error. These performance guarantees translate to minimax optimality in several instances, and experiments confirm superior performance of our algorithms over other baseline techniques.
Cite as

Syomantak Chaudhuri and Thomas A. Courtade. Private Estimation When Data and Privacy Demands Are Correlated. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 3:1-3:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chaudhuri_et_al:LIPIcs.FORC.2025.3,
  author =	{Chaudhuri, Syomantak and Courtade, Thomas A.},
  title =	{{Private Estimation When Data and Privacy Demands Are Correlated}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{3:1--3:20},
  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.2025.3},
  URN =		{urn:nbn:de:0030-drops-231305},
  doi =		{10.4230/LIPIcs.FORC.2025.3},
  annote =	{Keywords: Differential Privacy, Personalized Privacy, Heterogeneous Privacy, Correlations in Privacy}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.10
Count on Your Elders: Laplace vs Gaussian Noise

Authors: Joel Daniel Andersson, Rasmus Pagh, Teresa Anna Steiner, and Sahel Torkamani

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

Abstract
In recent years, Gaussian noise has become a popular tool in differentially private algorithms, often replacing Laplace noise which dominated the early literature on differential privacy. Gaussian noise is the standard approach to approximate differential privacy, often resulting in much higher utility than traditional (pure) differential privacy mechanisms. In this paper we argue that Laplace noise may in fact be preferable to Gaussian noise in many settings, in particular when we seek to achieve (ε,δ)-differential privacy for small values of δ. We consider two scenarios: First, we consider the problem of counting under continual observation and present a new generalization of the binary tree mechanism that uses a k-ary number system with negative digits to improve the privacy-accuracy trade-off. Our mechanism uses Laplace noise and whenever δ is sufficiently small it improves the mean squared error over the best possible (ε,δ)-differentially private factorization mechanisms based on Gaussian noise. Specifically, using k = 19 we get an asymptotic improvement over the bound given in the work by Henzinger, Upadhyay and Upadhyay (SODA 2023) when δ = O(T^{-0.92}). Second, we show that the noise added by the Gaussian mechanism can always be replaced by Laplace noise of comparable variance for the same (ε, δ)-differential privacy guarantee, and in fact for sufficiently small δ the variance of the Laplace noise becomes strictly better. This challenges the conventional wisdom that Gaussian noise should be used for high-dimensional noise. Finally, we study whether counting under continual observation may be easier in an average-case sense than in a worst-case sense. We show that, under pure differential privacy, the expected worst-case error for a random input must be Ω(log(T)/ε), matching the known lower bound for worst-case inputs.
Cite as

Joel Daniel Andersson, Rasmus Pagh, Teresa Anna Steiner, and Sahel Torkamani. Count on Your Elders: Laplace vs Gaussian Noise. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 10:1-10:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{andersson_et_al:LIPIcs.FORC.2025.10,
  author =	{Andersson, Joel Daniel and Pagh, Rasmus and Steiner, Teresa Anna and Torkamani, Sahel},
  title =	{{Count on Your Elders: Laplace vs Gaussian Noise}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{10:1--10:24},
  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.2025.10},
  URN =		{urn:nbn:de:0030-drops-231376},
  doi =		{10.4230/LIPIcs.FORC.2025.10},
  annote =	{Keywords: differential privacy, continual observation, streaming, prefix sums, trees}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.8
Differential Privacy Under Multiple Selections

Authors: Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, and Sahasrajit Sarmasarkar

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

Abstract
We consider the setting where a user with sensitive features wishes to obtain a recommendation from a server in a differentially private fashion. We propose a "multi-selection" architecture where the server can send back multiple recommendations and the user chooses one from these that matches best with their private features. When the user feature is one-dimensional - on an infinite line - and the accuracy measure is defined w.r.t some increasing function 𝔥(.) of the distance on the line, we precisely characterize the optimal mechanism that satisfies differential privacy. The specification of the optimal mechanism includes both the distribution of the noise that the user adds to its private value, and the algorithm used by the server to determine the set of results to send back as a response. We show that Laplace is an optimal noise distribution in this setting. Furthermore, we show that this optimal mechanism results in an error that is inversely proportional to the number of results returned when the function 𝔥(.) is the identity function.
Cite as

Ashish Goel, Zhihao Jiang, Aleksandra Korolova, Kamesh Munagala, and Sahasrajit Sarmasarkar. Differential Privacy Under Multiple Selections. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 8:1-8:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{goel_et_al:LIPIcs.FORC.2025.8,
  author =	{Goel, Ashish and Jiang, Zhihao and Korolova, Aleksandra and Munagala, Kamesh and Sarmasarkar, Sahasrajit},
  title =	{{Differential Privacy Under Multiple Selections}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{8:1--8:25},
  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.2025.8},
  URN =		{urn:nbn:de:0030-drops-231353},
  doi =		{10.4230/LIPIcs.FORC.2025.8},
  annote =	{Keywords: Differential Privacy, Mechanism Design and Multi-Selection}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.6
Near-Universally-Optimal Differentially Private Minimum Spanning Trees

Authors: Richard Hladík and Jakub Tětek

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

Abstract
Devising mechanisms with good beyond-worst-case input-dependent performance has been an important focus of differential privacy, with techniques such as smooth sensitivity, propose-test-release, or inverse sensitivity mechanism being developed to achieve this goal. This makes it very natural to use the notion of universal optimality in differential privacy. Universal optimality is a strong instance-specific optimality guarantee for problems on weighted graphs, which roughly states that for any fixed underlying (unweighted) graph, the algorithm is optimal in the worst-case sense, with respect to the possible setting of the edge weights. In this paper, we give the first such result in differential privacy. Namely, we prove that a simple differentially private mechanism for approximately releasing the minimum spanning tree is near-optimal in the sense of universal optimality for the 𝓁₁ neighbor relation. Previously, it was only known that this mechanism is nearly optimal in the worst case. We then focus on the 𝓁_∞ neighbor relation, for which the described mechanism is not optimal. We show that one may implement the exponential mechanism for MST in polynomial time, and that this results in universal near-optimality for both the 𝓁₁ and the 𝓁_∞ neighbor relations.
Cite as

Richard Hladík and Jakub Tětek. Near-Universally-Optimal Differentially Private Minimum Spanning Trees. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hladik_et_al:LIPIcs.FORC.2025.6,
  author =	{Hlad{\'\i}k, Richard and T\v{e}tek, Jakub},
  title =	{{Near-Universally-Optimal Differentially Private Minimum Spanning Trees}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{6:1--6:19},
  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.2025.6},
  URN =		{urn:nbn:de:0030-drops-231337},
  doi =		{10.4230/LIPIcs.FORC.2025.6},
  annote =	{Keywords: differential privacy, universal optimality, minimum spanning trees}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.1
Privacy-Computation Trade-Offs in Private Repetition and Metaselection

Authors: Kunal Talwar

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

Abstract
A Private Repetition algorithm takes as input a differentially private algorithm with constant success probability and boosts it to one that succeeds with high probability. These algorithms are closely related to private metaselection algorithms that compete with the best of many private algorithms, and private hyperparameter tuning algorithms that compete with the best hyperparameter settings for a private learning algorithm. Existing algorithms for these tasks pay either a large overhead in privacy cost, or a large overhead in computational cost. In this work, we show strong lower bounds for problems of this kind, showing in particular that for any algorithm that preserves the privacy cost up to a constant factor, the failure probability can only fall polynomially in the computational overhead. This is in stark contrast with the non-private setting, where the failure probability falls exponentially in the computational overhead. By carefully combining existing algorithms for metaselection, we prove computation-privacy tradeoffs that nearly match our lower bounds.
Cite as

Kunal Talwar. Privacy-Computation Trade-Offs in Private Repetition and Metaselection. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 1:1-1:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{talwar:LIPIcs.FORC.2025.1,
  author =	{Talwar, Kunal},
  title =	{{Privacy-Computation Trade-Offs in Private Repetition and Metaselection}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{1:1--1:14},
  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.2025.1},
  URN =		{urn:nbn:de:0030-drops-231282},
  doi =		{10.4230/LIPIcs.FORC.2025.1},
  annote =	{Keywords: Differential Privacy, Hyperparameter Tuning, Metaselection}
}
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