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Volume

LIPIcs, Volume 329

6th Symposium on Foundations of Responsible Computing (FORC 2025)

FORC 2025, June 4-6, 2025, Stanford University, CA, USA

Editors: Mark Bun

Document

DOI: 10.4230/LIPIcs.FORC.2026.10

Packing Compact Subgraphs with Applications to Districting

Authors: Ho-Lin Chen, Po-Yu Chou, Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu

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

Abstract

Packing disjoint subgraphs in a given graph is a fundamental problem with many applications. Motivated by political districting, we focus on connected subgraphs that are compact (e.g., having constant radius from a single center vertex) and that satisfy additional composition requirements, such as a minimum population/weight threshold or balanced weight types (e.g., political affiliations). We aim to maximize coverage by disjoint districts that meet these requirements. In this work, we present new results that substantially improve the previously known bounds on balanced star districts for planar and minor-free graphs [Prathamesh Dharangutte et al., 2025]. In particular, we improve the approximation factor from O(log n) to O(1) for packing balanced star districts using the exact same algorithm, but with a refined analysis. We also extend the results beyond planar graphs to minor-free graphs and an even broader family of graphs of bounded expansion. Additionally, we obtain an O(1) approximation for packing radius-k districts (with a constant k) in planar and apex-minor-free graphs. In order to get a (1+ε) approximation on the max coverage, we show that this can be achieved if we allow a slight relaxation of the balancedness parameters (by a factor that can be made arbitrarily close to 1), for bounded radius-k districts on planar and apex-minor-free graphs. We show that all of these results can also be obtained if we enforce a minimum weight threshold for each district as the composition requirement, rather than balancedness. We present various results on hardness and hardness of approximation for this variant, by graph and district types.

Cite as

Ho-Lin Chen, Po-Yu Chou, Prathamesh Dharangutte, Jie Gao, Shang-En Huang, and Fang-Yi Yu. Packing Compact Subgraphs with Applications to Districting. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 10:1-10:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{chen_et_al:LIPIcs.FORC.2026.10,
  author =	{Chen, Ho-Lin and Chou, Po-Yu and Dharangutte, Prathamesh and Gao, Jie and Huang, Shang-En and Yu, Fang-Yi},
  title =	{{Packing Compact Subgraphs with Applications to Districting}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{10:1--10:25},
  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.2026.10},
  URN =		{urn:nbn:de:0030-drops-259820},
  doi =		{10.4230/LIPIcs.FORC.2026.10},
  annote =	{Keywords: Approximation algorithms, algorithmic fairness}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.12

Tradeoffs in Privacy, Welfare, and Fairness for Facility Location

Authors: Sara Fish, Yannai A. Gonczarowski, Jason Z. Tang, and Salil Vadhan

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

Abstract

The differentially private (DP) facility location problem seeks to determine a socially optimal placement for a public facility while ensuring that each participating agent’s location remains private. In order to privatize its input data, a DP mechanism must inject noise into its output distribution, producing a placement that will have lower expected social welfare than the optimal spot for the facility. The privacy-induced welfare loss can be viewed as the "cost of privacy," illustrating a tradeoff between social welfare and privacy that has been the focus of prior work. Yet, the imposition of privacy also induces a third consideration that has not been similarly studied: fairness in how the "cost of privacy" is distributed across individuals. For instance, a mechanism may satisfy differential privacy with minimal social welfare loss, yet still be undesirable if that loss falls entirely on one individual. In this paper, we quantify this new notion of unfairness and design mechanisms for facility location that attempt to simultaneously optimize across these three objectives of privacy, social welfare, and fairness. Under this setup, we first derive an impossibility result, showing that privacy and fairness cannot be simultaneously guaranteed over all possible datasets that could represent the locations of individuals in a population. We then consider a relaxation of the original problem that still requires worst-case differential privacy, but only seeks fairness and appealing social welfare over smaller, more "realistic-looking" families of datasets. For this relaxation, we construct a DP mechanism and demonstrate that it is simultaneously optimal (or, for a harder family of datasets, near-optimal up to small factors) on fairness and social welfare. This suggests that while there is a tradeoff between privacy and each of social welfare and fairness, there is no additional tradeoff when we consider all three objectives simultaneously, provided that the population data is sufficiently natural.

Cite as

Sara Fish, Yannai A. Gonczarowski, Jason Z. Tang, and Salil Vadhan. Tradeoffs in Privacy, Welfare, and Fairness for Facility Location. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{fish_et_al:LIPIcs.FORC.2026.12,
  author =	{Fish, Sara and Gonczarowski, Yannai A. and Tang, Jason Z. and Vadhan, Salil},
  title =	{{Tradeoffs in Privacy, Welfare, and Fairness for Facility Location}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{12:1--12:22},
  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.2026.12},
  URN =		{urn:nbn:de:0030-drops-259858},
  doi =		{10.4230/LIPIcs.FORC.2026.12},
  annote =	{Keywords: differential privacy, facility location, fairness, mechanism design}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.3

Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms

Authors: Charlie Harrison and Pasin Manurangsi

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

Abstract

Zero-concentrated differential privacy (zCDP) is a variant of differential privacy (DP) that is widely used partly due to its nice composition property. While a tight conversion from ε-DP to zCDP exists for the worst-case mechanism, many common algorithms satisfy stronger guarantees. In this work, we derive tight zCDP characterizations for several fundamental mechanisms. We prove that the tight zCDP bound for the ε-DP Laplace mechanism is exactly ε + e^{-ε} - 1, confirming a recent conjecture by Wang [Yu-Xiang Wang, 2022]. We further provide tight bounds for the discrete Laplace mechanism, k-Randomized Response (for k ≤ 6), and RAPPOR. Lastly, we also provide a tight zCDP bound for the worst case bounded range mechanism.

Cite as

Charlie Harrison and Pasin Manurangsi. Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{harrison_et_al:LIPIcs.FORC.2026.3,
  author =	{Harrison, Charlie and Manurangsi, Pasin},
  title =	{{Exact zCDP Characterizations for Fundamental Differentially Private Mechanisms}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{3:1--3:18},
  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.2026.3},
  URN =		{urn:nbn:de:0030-drops-259741},
  doi =		{10.4230/LIPIcs.FORC.2026.3},
  annote =	{Keywords: Zero-Concentrated Differentially Privacy, Laplace Mechanism, Randomized Response}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.4

Nearly-Optimal Private Selection via Gaussian Mechanism

Authors: Ethan Leeman and Pasin Manurangsi

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

Abstract

Steinke [2025] recently asked the following intriguing open question: Can we solve the differentially private selection problem with nearly-optimal error by only (adaptively) invoking Gaussian mechanism on low-sensitivity queries? We resolve this question positively. In particular, for a candidate set 𝒴, we achieve error guarantee of Õ(log |𝒴|), which is within a factor of (log log |𝒴|)^{O(1)} of the exponential mechanism [McSherry and Talwar, 2007]. This improves on Steinke’s mechanism which achieves an error of O(log^{3/2} |𝒴|).

Cite as

Ethan Leeman and Pasin Manurangsi. Nearly-Optimal Private Selection via Gaussian Mechanism. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 4:1-4:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{leeman_et_al:LIPIcs.FORC.2026.4,
  author =	{Leeman, Ethan and Manurangsi, Pasin},
  title =	{{Nearly-Optimal Private Selection via Gaussian Mechanism}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{4:1--4:13},
  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.2026.4},
  URN =		{urn:nbn:de:0030-drops-259750},
  doi =		{10.4230/LIPIcs.FORC.2026.4},
  annote =	{Keywords: Differentially Private Selection, Gaussian Mechanism}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.17

Protecting the Undeleted in Machine Unlearning

Authors: Aloni Cohen, Refael Kohen, Kobbi Nissim, and Uri Stemmer

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

Abstract

Machine unlearning aims to remove specific data points from a trained model, often striving to emulate "perfect retraining", i.e., producing the model that would have been obtained had the deleted data never been included. We demonstrate that this approach, and security definitions that enable it, carry significant privacy risks for the remaining (undeleted) data points. We present a reconstruction attack showing that for certain tasks, which can be computed securely without deletions, a mechanism adhering to perfect retraining allows an adversary controlling merely ω(1) data points to reconstruct almost the entire dataset simply by issuing deletion requests. We survey existing definitions for machine unlearning, showing they are either susceptible to such attacks or too restrictive to support basic functionalities like exact summation. To address this problem, we propose a new security definition that specifically safeguards undeleted data against leakage caused by the deletion of other points. We show that our definition permits several essential functionalities, such as bulletin boards, summations, and statistical learning.

Cite as

Aloni Cohen, Refael Kohen, Kobbi Nissim, and Uri Stemmer. Protecting the Undeleted in Machine Unlearning. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 17:1-17:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{cohen_et_al:LIPIcs.FORC.2026.17,
  author =	{Cohen, Aloni and Kohen, Refael and Nissim, Kobbi and Stemmer, Uri},
  title =	{{Protecting the Undeleted in Machine Unlearning}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{17:1--17:18},
  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.2026.17},
  URN =		{urn:nbn:de:0030-drops-259901},
  doi =		{10.4230/LIPIcs.FORC.2026.17},
  annote =	{Keywords: Unlearning, data deletion, privacy}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.18

A Differentially Private Approximation of the Width Problem

Authors: Mor Hale and Or Sheffet

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

Abstract

The width of a point set - the minimum distance between two parallel hyperplanes enclosing the data - is a fundamental geometric measure that captures how "flat" or "fat" a dataset is. As such, it serves as a basic shape descriptor used in visualization, convex hull approximation, and geometric data analysis. Despite its importance, width is highly sensitive to single-point changes, and no differentially private algorithm for approximating it was previously known. We present the first pure ε-differentially private algorithm that approximates the width of a dataset. Our algorithm is a private adaptation of Chan’s approximation scheme [Chan, 2000] and operates by privately approximating the solution to a collection of suitably formulated linear programs. In addition to estimating the width, our method privately identifies a corresponding direction, enabling a private "fattening" transformation of the dataset - a basic structural preprocessing step for many geometric algorithms. This work advances the understanding of how geometric shape descriptors can admit good approximations even under the constraints of differential privacy.

Cite as

Mor Hale and Or Sheffet. A Differentially Private Approximation of the Width Problem. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{hale_et_al:LIPIcs.FORC.2026.18,
  author =	{Hale, Mor and Sheffet, Or},
  title =	{{A Differentially Private Approximation of the Width Problem}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{18:1--18:18},
  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.2026.18},
  URN =		{urn:nbn:de:0030-drops-259914},
  doi =		{10.4230/LIPIcs.FORC.2026.18},
  annote =	{Keywords: Differential privacy, computational geometry, width approximation, private algorithms}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.20

Privacy, Prediction, and Allocation

Authors: Ben Jacobsen and Nitin Kohli

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

Abstract

Algorithmic predictions are increasingly used to inform the allocation of scarce resources. The promise of these methods is that, through machine learning, they can better identify the people who would benefit most from interventions. Recently, however, several works have called this assumption into question by demonstrating the existence of settings where simple, unit-level allocation strategies can meet or even exceed the performance of those based on individual-level targeting. Separately, other works have objected to individual-level targeting on privacy grounds, leading to an unusual situation where a single solution, unit-level targeting, is recommended for reasons of both privacy and utility. Motivated by the desire to fully understand the interplay of privacy and targeting levels, we initiate the study of aid allocation systems that satisfy differential privacy, synthesizing existing works on private optimization with the economic models of aid allocation used in the non-private literature. To this end, we investigate private variants of both individual and unit-level allocation strategies in both stochastic and distribution-free settings under a range of constraints on data availability. Through this analysis, we provide clean, interpretable bounds characterizing the tradeoffs between privacy, efficiency, and targeting precision in allocation.

Cite as

Ben Jacobsen and Nitin Kohli. Privacy, Prediction, and Allocation. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 20:1-20:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{jacobsen_et_al:LIPIcs.FORC.2026.20,
  author =	{Jacobsen, Ben and Kohli, Nitin},
  title =	{{Privacy, Prediction, and Allocation}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{20:1--20:24},
  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.2026.20},
  URN =		{urn:nbn:de:0030-drops-259935},
  doi =		{10.4230/LIPIcs.FORC.2026.20},
  annote =	{Keywords: Differential privacy, fair allocation, limits of prediction}
}

Document

DOI: 10.4230/LIPIcs.FORC.2026.22

Separating Oblivious and Adaptive Differential Privacy Under Continual Observation

Authors: Mark Bun, Marco Gaboardi, and Connor Wagaman

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

Abstract

We resolve an open question of Jain, Raskhodnikova, Sivakumar, and Smith (ICML 2023) by exhibiting a problem separating differential privacy under continual observation in the oblivious and adaptive settings. The continual observation (a.k.a. continual release) model formalizes privacy for streaming algorithms, where data is received over time and output is released at each time step. In the oblivious setting, privacy need only hold for data streams fixed in advance; in the adaptive setting, privacy is required even for streams that can be chosen adaptively based on the streaming algorithm’s output. We describe the first explicit separation between the oblivious and adaptive settings. The problem showing this separation is based on the correlated vector queries problem of Bun, Steinke, and Ullman (SODA 2017). Specifically, we present an (ε,0)-DP algorithm for the oblivious setting that remains accurate for exponentially many time steps in the dimension of the input. On the other hand, we show that every (ε,δ)-DP adaptive algorithm fails to be accurate after releasing output for only a constant number of time steps.

Cite as

Mark Bun, Marco Gaboardi, and Connor Wagaman. Separating Oblivious and Adaptive Differential Privacy Under Continual Observation. In 7th Symposium on Foundations of Responsible Computing (FORC 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 368, pp. 22:1-22:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{bun_et_al:LIPIcs.FORC.2026.22,
  author =	{Bun, Mark and Gaboardi, Marco and Wagaman, Connor},
  title =	{{Separating Oblivious and Adaptive Differential Privacy Under Continual Observation}},
  booktitle =	{7th Symposium on Foundations of Responsible Computing (FORC 2026)},
  pages =	{22:1--22:11},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-259959},
  doi =		{10.4230/LIPIcs.FORC.2026.22},
  annote =	{Keywords: differential privacy, continual observation, continual release, streaming algorithms, adaptive algorithms}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.35

A Quantum Pigeonhole Principle and Two Semidefinite Relaxations of Communication Complexity

Authors: Pavel Dvořák, Bruno Loff, and Suhail Sherif

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

Abstract

We are interested in what happens when we take a Π₁ combinatorial statement, write its negation as a homogeneous quadratic feasibility problem (HQFP), and relax the problem into a positive semidefinite feasibility problem. This question is particularly interesting owing to the fact that any statement written as a PSD feasibility problem can be proven or disproven using a short proof. We investigate this for one very simple and one very complicated statement. The simple statement we look at is the pigeonhole principle. We prove that the relaxed negation of the PHP remains unsatisfiable and we thus obtain a new "quantum" pigeonhole principle (QPHP) which is a stronger statement than the vanilla PHP. It states that if we take n copies of the same state, and measure each copy using a measurement with only n-1 outcomes (the measurement can be different for different copies), then there will be an outcome j and two copies i₁, i₂ where the resulting states, obtained when the outcome is j for both copies, are not orthogonal. We then look at the statement "the deterministic communication complexity of f is ≤ k", where f could be either a function or a relation. We write this statement in two equivalent ways, using two different HQFPs. By relaxing to PSD feasibility, we increase the set of available protocols, and thus we always get a communication model which is stronger than deterministic communication complexity. An argument from proof complexity shows that any model obtained in this way will solve all Karchmer-Wigderson games efficiently. However, the argument is very indirect and does not give us an explicit protocol that solves the Karchmer-Wigderson games. We then work to find such protocols in the two communication models obtained by relaxing our two formulations. When relaxing the first of the two formulations we obtain a structured variant of the γ₂ norm. This communication model is to subunit γ₂ norm matrices like deterministic protocols are to rectangles, and so we call the protocols in this model γ₂ protocols. We show that log-inverse-discrepancy is a lower-bound for this model. We then show how to compute equality (deterministically) using O(1) bits of γ₂-communication, which implies that KW games are easy in the model. When relaxing the second of the two formulations we obtain what we call quantum lab protocols. This model happens to have a functional description, wherein Alice and Bob communicate solely via the outcomes of binary measurements of a shared quantum state (whose initial state is independent of the inputs). They are required to give the correct output with zero error probability. We use our QPHP to prove a lower-bound of n against two-round quantum lab protocols for equality. However we also show that any Boolean function f can be computed in three rounds and four measurements.

Cite as

Pavel Dvořák, Bruno Loff, and Suhail Sherif. A Quantum Pigeonhole Principle and Two Semidefinite Relaxations of Communication Complexity. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{dvorak_et_al:LIPIcs.STACS.2026.35,
  author =	{Dvo\v{r}\'{a}k, Pavel and Loff, Bruno and Sherif, Suhail},
  title =	{{A Quantum Pigeonhole Principle and Two Semidefinite Relaxations of Communication Complexity}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{35:1--35:20},
  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.2026.35},
  URN =		{urn:nbn:de:0030-drops-255243},
  doi =		{10.4230/LIPIcs.STACS.2026.35},
  annote =	{Keywords: Proofs, Semidefinite Programs, Quantum Pigeonhole Principle, Communication Complexity}
}

Document

DOI: 10.4230/LIPIcs.STACS.2026.66

Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds

Authors: Yupan Liu

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

Abstract

We investigate the computational hardness of estimating the quantum α-Rényi entropy S^𝚁_α(ρ) = (ln Tr(ρ^α))/(1-α) and the quantum q-Tsallis entropy S^𝚃_q(ρ) = (1-Tr(ρ^q))/(q-1), both converging to the von Neumann entropy as the order approaches 1. The promise problems Quantum α-Rényi Entropy Approximation (RényiQEA_α) and Quantum q-Tsallis Entropy Approximation (TsallisQEA_q) ask whether S^𝚁_α(ρ) or S^𝚃_q(ρ), respectively, is at least τ_Y or at most τ_N, where τ_Y - τ_N is typically a positive constant. Previous hardness results cover only the von Neumann entropy (order 1) and some cases of the quantum q-Tsallis entropy, while existing approaches do not readily extend to other orders. We establish that for all positive real orders, the rank-2 variants Rank2RényiQEA_α and Rank2TsallisQEA_q are BQP-hard. Combined with prior (rank-dependent) quantum query algorithms in Wang, Guan, Liu, Zhang, and Ying (TIT 2024), Wang, Zhang, and Li (TIT 2024), and Liu and Wang (SODA 2025), our results imply: - For all real order α > 0 and 0 < q ≤ 1, LowRankRényiQEA_α and LowRankTsallisQEA_q are BQP-complete, where both are restricted versions of RényiQEA_α and TsallisQEA_q with ρ of polynomial rank. - For all real order q > 1, TsallisQEA_q is BQP-complete. Our hardness results stem from reductions based on new inequalities relating the α-Rényi or q-Tsallis binary entropies of different orders, where the reductions differ substantially from previous approaches, and the inequalities are also of independent interest.

Cite as

Yupan Liu. Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 66:1-66:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu:LIPIcs.STACS.2026.66,
  author =	{Liu, Yupan},
  title =	{{Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{66:1--66:23},
  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.2026.66},
  URN =		{urn:nbn:de:0030-drops-255550},
  doi =		{10.4230/LIPIcs.STACS.2026.66},
  annote =	{Keywords: computational hardness, quantum state testing, quantum R\'{e}nyi entropy, quantum Tsallis entropy, von Neumann entropy}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2026.88

Lower Bounds and Separations for Torus Polynomials

Authors: Vaibhav Krishan and Sundar Vishwanathan

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

Abstract

The class ACC⁰ consists of Boolean functions that can be computed by constant-depth circuits of polynomial size with AND, NOT and MOD_m gates, where m is a natural number. At the frontier of our understanding lies a widely believed conjecture asserting that MAJORITY does not belong to ACC⁰. A few years ago, Bhrushundi, Hosseini, Lovett and Rao (ITCS 2019) introduced torus polynomial approximations as an approach towards this conjecture. Torus polynomials approximate Boolean functions when the fractional part of their value on Boolean points is close to half the value of the function. They reduced the conjecture that MAJORITY ∉ ACC⁰ to a conjecture concerning the non-existence of low degree torus polynomials that approximate MAJORITY. We reduce the non-existence problem further, to a statement about finding feasible solutions for an infinite family of linear programs. The main advantage of this statement is that it allows for incremental progress, which means finding feasible solutions for successively larger collections of these programs. As an immediate first step, we find feasible solutions for a large class of these linear programs, leaving only a finite set for further consideration. Our method is inspired by the method of dual polynomials, which is used to study the approximate degree of Boolean functions. Using our method, we also propose a way to progress further. We prove several additional key results with the same method, which include: - A lower bound on the degree of symmetric torus polynomials that approximate the AND function. As a consequence, we get a separation that symmetric torus polynomials are weaker than their asymmetric counterparts. - An error-degree trade-off for symmetric torus polynomials approximating the MAJORITY function, strengthening the corresponding result of Bhrushundi, Hosseini, Lovett and Rao (ITCS 2019). - The first lower bounds against torus polynomials approximating AND, showcasing the power of the machinery we develop. This lower bound nearly matches the corresponding upper bound. Hence, we get an almost complete characterization of the torus polynomial approximation degree of AND. - Lower bounds against asymmetric torus polynomials approximating MAJORITY, or AND, in the very low error regime. This partially answers a question posed in Bhrushundi, Hosseini, Lovett and Rao (ITCS 2019) about error-reduction for torus polynomials.

Cite as

Vaibhav Krishan and Sundar Vishwanathan. Lower Bounds and Separations for Torus Polynomials. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 88:1-88:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{krishan_et_al:LIPIcs.ITCS.2026.88,
  author =	{Krishan, Vaibhav and Vishwanathan, Sundar},
  title =	{{Lower Bounds and Separations for Torus Polynomials}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{88:1--88:20},
  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.2026.88},
  URN =		{urn:nbn:de:0030-drops-253751},
  doi =		{10.4230/LIPIcs.ITCS.2026.88},
  annote =	{Keywords: Circuit complexity, ACC, lower bounds, polynomials}
}

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.

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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.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.2026.22

Simplicial Covering Dimension of Extremal Concept Classes

Authors: Ari Blondal, Hamed Hatami, Pooya Hatami, Chavdar Lalov, and Sivan Tretiak

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

Abstract

Dimension theory is a branch of topology concerned with defining and analyzing dimensions of geometric and topological spaces in purely topological terms. In this work, we adapt the classical notion of topological dimension (Lebesgue covering) to binary concept classes. The topological space naturally associated with a concept class is its space of realizable distributions. The loss function and the class itself induce a simplicial structure on this space, with respect to which we define a simplicial covering dimension. We prove that for finite concept classes, this simplicial covering dimension exactly characterizes the list replicability number (equivalently, global stability) in PAC learning. This connection allows us to apply tools from classical dimension theory to compute the exact list replicability number of the broad family of extremal concept classes.

Cite as

Ari Blondal, Hamed Hatami, Pooya Hatami, Chavdar Lalov, and Sivan Tretiak. Simplicial Covering Dimension of Extremal Concept Classes. In 17th Innovations in Theoretical Computer Science Conference (ITCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 362, pp. 22:1-22:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{blondal_et_al:LIPIcs.ITCS.2026.22,
  author =	{Blondal, Ari and Hatami, Hamed and Hatami, Pooya and Lalov, Chavdar and Tretiak, Sivan},
  title =	{{Simplicial Covering Dimension of Extremal Concept Classes}},
  booktitle =	{17th Innovations in Theoretical Computer Science Conference (ITCS 2026)},
  pages =	{22:1--22:24},
  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.2026.22},
  URN =		{urn:nbn:de:0030-drops-253094},
  doi =		{10.4230/LIPIcs.ITCS.2026.22},
  annote =	{Keywords: PAC Learning, Extremal Concept Classes, Replicability, List Replicability, Topology, Geometry}
}

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