24 Search Results for "Stemmer, Uri"

Document
DOI: 10.4230/LIPIcs.ITCS.2026.40
A Simple and Robust Protocol for Distributed Counting

Authors: Edith Cohen, Moshe Shechner, and Uri Stemmer

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

Abstract
We revisit the distributed counting problem, where a server must continuously approximate the total number of events occurring across k sites while minimizing communication. The communication complexity of this problem is known to be Θ(k/(ε)log N) for deterministic protocols. Huang, Yi, and Zhang (2012) showed that randomization can reduce this to Θ((√k)/ε log N), but their analysis is restricted to the oblivious setting, where the stream of events is independent of the protocol’s outputs. Xiong, Zhu, and Huang (2023) presented a robust protocol for distributed counting that removes the oblivious assumption. However, their communication complexity is suboptimal by a polylog(k) factor and their protocol is substantially more complex than the oblivious protocol of Huang et al. (2012). This left open a natural question: could it be that the simple protocol of Huang et al. (2012) is already robust? We resolve this question with two main contributions. First, we show that the protocol of Huang et al. (2012) is itself not robust by constructing an explicit adaptive attack that forces it to lose its accuracy. Second, we present a new, surprisingly simple, robust protocol for distributed counting that achieves the optimal communication complexity of O((√k)/ε log N). Our protocol is simpler than that of Xiong et al. (2023), perhaps even simpler than that of Huang et al. (2012), and is the first to match the optimal oblivious complexity in the adaptive setting.
Cite as

Edith Cohen, Moshe Shechner, and Uri Stemmer. A Simple and Robust Protocol for Distributed Counting. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 40:1-40:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cohen_et_al:LIPIcs.ITCS.2026.40,
  author =	{Cohen, Edith and Shechner, Moshe and Stemmer, Uri},
  title =	{{A Simple and Robust Protocol for Distributed Counting}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{40:1--40:24},
  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.2026.40},
  URN =		{urn:nbn:de:0030-drops-253272},
  doi =		{10.4230/LIPIcs.ITCS.2026.40},
  annote =	{Keywords: Distributed Streaming, Adversarial Streaming}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.84
Bayesian Perspective on Memorization and Reconstruction

Authors: Haim Kaplan, Yishay Mansour, Kobbi Nissim, and Uri Stemmer

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

Abstract
We introduce a new Bayesian perspective on the concept of data reconstruction, and leverage this viewpoint to propose a new security definition that, in certain settings, provably prevents reconstruction attacks. We use our paradigm to shed new light on one of the most notorious attacks in the privacy and memorization literature - fingerprinting code attacks (FPC). We argue that these attacks are really a form of membership inference attacks, rather than reconstruction attacks. Furthermore, we show that if the goal is solely to prevent reconstruction (but not membership inference), then in some cases the impossibility results derived from FPC no longer apply.
Cite as

Haim Kaplan, Yishay Mansour, Kobbi Nissim, and Uri Stemmer. Bayesian Perspective on Memorization and Reconstruction. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 84:1-84:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{kaplan_et_al:LIPIcs.ITCS.2026.84,
  author =	{Kaplan, Haim and Mansour, Yishay and Nissim, Kobbi and Stemmer, Uri},
  title =	{{Bayesian Perspective on Memorization and Reconstruction}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{84:1--84:18},
  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.2026.84},
  URN =		{urn:nbn:de:0030-drops-253713},
  doi =		{10.4230/LIPIcs.ITCS.2026.84},
  annote =	{Keywords: Reconstruction, Memorization, Differential privacy}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.16
Robust Streaming Against Low-Memory Adversaries

Authors: Omri Ben-Eliezer, Krzysztof Onak, and Sandeep Silwal

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

Abstract
Robust streaming, the study of streaming algorithms that provably work when the stream is generated by an adaptive adversary, has seen tremendous progress in recent years. However, fundamental barriers remain: the best known algorithm for turnstile F_p-estimation in the robust streaming setting is exponentially worse than in the oblivious setting, and closing this gap seems difficult. Arguably, one possible cause of this barrier is the adversarial model, which may be too strong: unlike the space-bounded streaming algorithm, the adversary can memorize the entire history of the interaction with the algorithm. Can we then close the exponential gap if we insist that the adversary itself is an adaptive but low-memory entity, roughly as powerful as (or even weaker than) the algorithm? In this work we present the first set of models and results aimed towards this question. We design efficient robust streaming algorithms against adversaries that are fully adaptive but have no long-term memory ("memoryless") or very little memory of the history of interaction. Roughly speaking, a memoryless adversary only sees, at any given round, the last output of the algorithm (and does not even know the current time) and can generate an unlimited number of independent coin tosses. A low-memory adversary is similar, but maintains an additional small buffer. While these adversaries may seem quite limited at first glance, we show that this adversarial model is strong enough to produce streams that have high flip number and density in the context of F₂-estimation, which rules out most known robustification techniques. We then design a new simple approach, similar to the computation paths framework, to obtain efficient algorithms against memoryless and low-memory adversaries for a wide class of order-invariant problems. We conclude by posing various open questions proposing further exploration of the landscape of robust streaming against fully adaptive but computationally constrained adversaries.
Cite as

Omri Ben-Eliezer, Krzysztof Onak, and Sandeep Silwal. Robust Streaming Against Low-Memory Adversaries. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 16:1-16:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{beneliezer_et_al:LIPIcs.ITCS.2026.16,
  author =	{Ben-Eliezer, Omri and Onak, Krzysztof and Silwal, Sandeep},
  title =	{{Robust Streaming Against Low-Memory Adversaries}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{16:1--16:23},
  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.2026.16},
  URN =		{urn:nbn:de:0030-drops-253037},
  doi =		{10.4230/LIPIcs.ITCS.2026.16},
  annote =	{Keywords: robust streaming, adaptive robustness, bounded-space adversaries}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2026.64
Optimal White-Box Adversarial Streaming Lower Bounds for Approximating LIS Length

Authors: Anna Gal, Gillat Kol, Raghuvansh R. Saxena, and Huacheng Yu

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

Abstract
The space complexity of deterministic streaming algorithms for approximating the length of the longest increasing subsequence (LIS) in a string of length n has been known to be Θ̃(√n) for almost two decades. In contrast, the space complexity of this problem for randomized streaming algorithms remains one of the few longstanding open problems in one-pass streaming. In fact, no better than Ω(log n) lower bounds are known, and the best upper bounds are no better than their deterministic counterparts. In this paper, we push the limits of our understanding of the streaming space complexity of the approximate LIS length problem by studying it in the white-box adversarial streaming model. This model is an intermediate model between deterministic and randomized streaming algorithms that has recently attracted attention. In the white-box model, the streaming algorithm can draw fresh randomness when processing each incoming element, but an adversary generating the stream observes all previously used randomness and adaptively chooses the subsequent elements of the stream. We prove a tight (up to logarithmic factors) Ω(√n) space lower bound for any white-box streaming algorithm that approximates the length of the LIS of a stream of length n to within a factor better than 1.1. Thus, for this problem, white-box algorithms offer no improvement over deterministic ones.
Cite as

Anna Gal, Gillat Kol, Raghuvansh R. Saxena, and Huacheng Yu. Optimal White-Box Adversarial Streaming Lower Bounds for Approximating LIS Length. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 64:1-64:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{gal_et_al:LIPIcs.ITCS.2026.64,
  author =	{Gal, Anna and Kol, Gillat and Saxena, Raghuvansh R. and Yu, Huacheng},
  title =	{{Optimal White-Box Adversarial Streaming Lower Bounds for Approximating LIS Length}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{64:1--64:17},
  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.2026.64},
  URN =		{urn:nbn:de:0030-drops-253519},
  doi =		{10.4230/LIPIcs.ITCS.2026.64},
  annote =	{Keywords: White-bos streaming, Longest increasing subsequence}
}
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
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.77
Minimizing Recourse in an Adaptive Balls and Bins Game

Authors: Adi Fine, Haim Kaplan, and Uri Stemmer

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We consider a simple load-balancing game between an algorithm and an adaptive adversary. In a simplified version of this game, the adversary observes the assignment of jobs to machines and selects a machine to kill. The algorithm must then restart the jobs from the failed machine on other machines. The adversary repeats this process, observing the new assignment and eliminating another machine, and so on. The adversary aims to force the algorithm to perform many restarts, while we seek a robust algorithm that minimizes restarts regardless of the adversary’s strategy. This game was recently introduced by Bhattacharya et al. for designing a 3-spanner with low recourse against an adaptive adversary. We prove that a simple algorithm, which assigns each job to a randomly chosen live bin, incurs O(n log n) recourse against an adaptive adversary. This enables us to construct a much simpler 3-spanner with a recourse that is smaller by a factor of O(log² n) compared to the previous construction, without increasing the update time or the size of the spanner. This motivates a careful examination of the range of attacks an adaptive adversary can deploy against simple algorithms before resorting to more complex ones. As our case study demonstrates, this attack space may not be as large as it initially appears, enabling the development of robust algorithms that are both simpler and easier to analyze.
Cite as

Adi Fine, Haim Kaplan, and Uri Stemmer. Minimizing Recourse in an Adaptive Balls and Bins Game. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 77:1-77:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{fine_et_al:LIPIcs.ICALP.2025.77,
  author =	{Fine, Adi and Kaplan, Haim and Stemmer, Uri},
  title =	{{Minimizing Recourse in an Adaptive Balls and Bins Game}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{77:1--77:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.77},
  URN =		{urn:nbn:de:0030-drops-234544},
  doi =		{10.4230/LIPIcs.ICALP.2025.77},
  annote =	{Keywords: Adaptive adversary, load-balancing game, balls-and-bins, randomized algorithms, dynamic 3-spanner, dynamic graph algorithms, adversarial robustness}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.106
Streaming Maximal Matching with Bounded Deletions

Authors: Sanjeev Khanna, Christian Konrad, and Jacques Dark

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We initiate the study of the Maximal Matching problem in bounded-deletion graph streams. In this setting, a graph G is revealed as an arbitrary sequence of edge insertions and deletions, where the number of insertions is unrestricted but the number of deletions is guaranteed to be at most K, for some given parameter K. The single-pass streaming space complexity of this problem is known to be Θ(n²) when K is unrestricted, where n is the number of vertices of the input graph. In this work, we present new randomized and deterministic algorithms and matching lower bound results that together give a tight understanding (up to poly-log factors) of how the space complexity of Maximal Matching evolves as a function of the parameter K: The randomized space complexity of this problem is Θ̃(n ⋅ √K), while the deterministic space complexity is Θ̃(n ⋅ K). We further show that if we relax the maximal matching requirement to an α-approximation to Maximum Matching, for any constant α > 2, then the space complexity for both, deterministic and randomized algorithms, strikingly changes to Θ̃(n + K). A key conceptual contribution of our work that underlies all our algorithmic results is the introduction of the hierarchical maximal matching data structure, which computes a hierarchy of L maximal matchings on the substream of edge insertions, for an integer L. This deterministic data structure allows recovering a Maximal Matching even in the presence of up to L-1 edge deletions, which immediately yields an optimal deterministic algorithm with space Õ(n ⋅ K). To reduce the space to Õ(n ⋅ √K), we compute only √K levels of our hierarchical matching data structure and utilize a randomized linear sketch, i.e., our matching repair data structure, to repair any damage due to edge deletions. Using our repair data structure, we show that the level that is least affected by deletions can be repaired back to be globally maximal. The repair data structure is computed independently of the hierarchical maximal matching data structure and stores information for vertices at different scales with a gradually smaller set of vertices storing more and more information about their incident edges. The repair process then makes progress either by rematching a vertex to a previously unmatched vertex, or by strategically matching it to another matched vertex whose current mate is in a better position to find a new mate in that we have stored more information about its incident edges. Our lower bound result for randomized algorithms is obtained by establishing a lower bound for a generalization of the well-known Augmented-Index problem in the one-way two-party communication setting that we refer to as Embedded-Augmented-Index, and then showing that an instance of Embedded-Augmented-Index reduces to computing a maximal matching in bounded-deletion streams. To obtain our lower bound for deterministic algorithms, we utilize a compression argument to show that a deterministic algorithm with space o(n ⋅ K) would yield a scheme to compress a suitable class of graphs below the information-theoretic threshold.
Cite as

Sanjeev Khanna, Christian Konrad, and Jacques Dark. Streaming Maximal Matching with Bounded Deletions. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 106:1-106:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{khanna_et_al:LIPIcs.ICALP.2025.106,
  author =	{Khanna, Sanjeev and Konrad, Christian and Dark, Jacques},
  title =	{{Streaming Maximal Matching with Bounded Deletions}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{106:1--106:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.106},
  URN =		{urn:nbn:de:0030-drops-234834},
  doi =		{10.4230/LIPIcs.ICALP.2025.106},
  annote =	{Keywords: Streaming Algorithms, Maximal Matching, Maximum Matching, Bounded-Deletion Streams}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.6
Decremental (1+ε)-Approximate Maximum Eigenvector: Dynamic Power Method

Authors: Deeksha Adil and Thatchaphol Saranurak

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We present a dynamic algorithm for maintaining (1+ε)-approximate maximum eigenvector and eigenvalue of a positive semi-definite matrix A undergoing decreasing updates, i.e., updates which may only decrease eigenvalues. Given a vector v updating A ← A-vv^⊤, our algorithm takes Õ(nnz(v)) amortized update time, i.e., polylogarithmic per non-zeros in the update vector. Our technique is based on a novel analysis of the influential power method in the dynamic setting. The two previous sets of techniques have the following drawbacks (1) algebraic techniques can maintain exact solutions but their update time is at least polynomial per non-zeros, and (2) sketching techniques admit polylogarithmic update time but suffer from a crude additive approximation. Our algorithm exploits an oblivious adversary. Interestingly, we show that any algorithm with polylogarithmic update time per non-zeros that works against an adaptive adversary and satisfies an additional natural property would imply a breakthrough for checking psd-ness of matrices in Õ(n²) time, instead of O(n^ω) time.
Cite as

Deeksha Adil and Thatchaphol Saranurak. Decremental (1+ε)-Approximate Maximum Eigenvector: Dynamic Power Method. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{adil_et_al:LIPIcs.ICALP.2025.6,
  author =	{Adil, Deeksha and Saranurak, Thatchaphol},
  title =	{{Decremental (1+\epsilon)-Approximate Maximum Eigenvector: Dynamic Power Method}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.6},
  URN =		{urn:nbn:de:0030-drops-233834},
  doi =		{10.4230/LIPIcs.ICALP.2025.6},
  annote =	{Keywords: Power Method, Dynamic Algorithms}
}
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}
}
Document
DOI: 10.4230/LIPIcs.FORC.2025.23
The Correlated Gaussian Sparse Histogram Mechanism

Authors: Christian Janos Lebeda and Lukas Retschmeier

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

Abstract
We consider the problem of releasing a sparse histogram under (ε, δ)-differential privacy. The stability histogram independently adds noise from a Laplace or Gaussian distribution to the non-zero entries and removes those noisy counts below a threshold. Thereby, the introduction of new non-zero values between neighboring histograms is only revealed with probability at most δ, and typically, the value of the threshold dominates the error of the mechanism. We consider the variant of the stability histogram with Gaussian noise. Recent works ([Joseph and Yu, COLT '24] and [Lebeda, SOSA '25]) reduced the error for private histograms using correlated Gaussian noise. However, these techniques can not be directly applied in the very sparse setting. Instead, we adopt Lebeda’s technique and show that adding correlated noise to the non-zero counts only allows us to reduce the magnitude of noise when we have a sparsity bound. This, in turn, allows us to use a lower threshold by up to a factor of 1/2 compared to the non-correlated noise mechanism. We then extend our mechanism to a setting without a known bound on sparsity. Additionally, we show that correlated noise can give a similar improvement for the more practical discrete Gaussian mechanism.
Cite as

Christian Janos Lebeda and Lukas Retschmeier. The Correlated Gaussian Sparse Histogram Mechanism. In 6th Symposium on Foundations of Responsible Computing (FORC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 329, pp. 23:1-23:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{lebeda_et_al:LIPIcs.FORC.2025.23,
  author =	{Lebeda, Christian Janos and Retschmeier, Lukas},
  title =	{{The Correlated Gaussian Sparse Histogram Mechanism}},
  booktitle =	{6th Symposium on Foundations of Responsible Computing (FORC 2025)},
  pages =	{23:1--23:20},
  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.2025.23},
  URN =		{urn:nbn:de:0030-drops-231503},
  doi =		{10.4230/LIPIcs.FORC.2025.23},
  annote =	{Keywords: differential privacy, correlated noise, sparse gaussian histograms}
}
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