Pasin Manurangsi
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Rank aggregation is a task of combining the rankings of items from multiple users into a single ranking that best represents the users' rankings. Alabi et al. (AAAI'22) presents differentially-private (DP) polynomial-time approximation schemes (PTASes) and 5-approximation algorithms with certain additive errors for the Kemeny rank aggregation problem in both central and local models. In this paper, we present improved DP PTASes with smaller additive error in the central model. Furthermore, we are first to study the footrule rank aggregation problem under DP. We give a near-optimal algorithm for this problem; as a corollary, this leads to 2-approximation algorithms with the same additive error as the 5-approximation algorithms of Alabi et al. for the Kemeny rank aggregation problem in both central and local models.
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We study the fair allocation of indivisible goods with variable groups. In this model, the goal is to partition the agents into groups of given sizes and allocate the goods to the groups in a fair manner. We show that for any number of groups and corresponding sizes, there always exists an envy-free up to one good (EF1) outcome, thereby generalizing an important result from the individual setting. Our result holds for arbitrary monotonic utilities and comes with an efficient algorithm. We also prove that the EF1 existence can be guaranteed even when the goods lie on a path and each group must receive a connected bundle. In addition, we consider a probabilistic model where the utilities are additive and drawn randomly from a distribution. We show that if there are n agents and the number of goods m is divisible by the number of groups k, then an envy-free outcome exists with high probability if m = ω(log n), and this bound is tight. On the other hand, if m is not divisible by k, then an envy-free outcome is unlikely to exist as long as m = o(√n).
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We consider a setting where we have a ground set ℳ together with real-valued set functions f₁, … , f_n, and the goal is to partition ℳ into two sets S₁,S₂ such that |f_i(S₁) - f_i(S₂)| is small for every i. Many results in discrepancy theory can be stated in this form with the functions f_i being additive. In this work, we initiate the study of the unstructured case where f_i is not assumed to be additive. We show that even without the additivity assumption, the upper bound remains at most O(√{n log n}).
Our result has implications on the fair allocation of indivisible goods. In particular, we show that a consensus halving up to O(√{n log n}) goods always exists for n agents with monotone utilities. Previously, only an O(n) bound was known for this setting.
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We prove the following asymptotically tight lower bound for k-color discrepancy: For any k ≥ 2, there exists a hypergraph with n vertices such that its k-color discrepancy is at least Ω(√n). This improves on the previously known lower bound of Ω(√n/ log k) due to Caragiannis et al. [CLS25]. As an application, we show that our result implies improved lower bounds for group fair division.
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We study the d-dimensional knapsack problem. We are given a set of items, each with a d-dimensional cost vector and a profit, along with a d-dimensional budget vector. The goal is to select a set of items that do not exceed the budget in all dimensions and maximize the total profit. A polynomial-time approximation scheme (PTAS) with running time n^{Θ(d/{ε})} has long been known for this problem, where {ε} is the error parameter and n is the encoding size. Despite decades of active research, the best running time of a PTAS has remained O(n^{⌈ d/{ε} ⌉ - d}). Unfortunately, existing lower bounds only cover the special case with two dimensions d = 2, and do not answer whether there is a n^{o(d/({ε)})}-time PTAS for larger values of d.
In this work, we show that the running times of the best-known PTAS cannot be improved up to a polylogarithmic factor assuming the Exponential Time Hypothesis (ETH). Our techniques are based on a robust reduction from 2-CSP, which embeds 2-CSP constraints into a desired number of dimensions. Then, using a recent result of [Bafna Karthik and Minzer, STOC'25], we succeed in exhibiting tight trade-off between d and {ε} for all regimes of the parameters assuming d is sufficiently large. Informally, our result also shows that under ETH, for any function f there is no f(d/({ε)}) ⋅ n^{õ(d/({ε)})}-time (1-{ε})-approximation for d-dimensional knapsack, where n is the number of items and õ hides polylogarithmic factors in d/({ε)}.
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How Unique is Whose Web Browser? The role of demographics in browser fingerprinting
Pritish Kamath
Robin Lassonde
Proceedings on Privacy Enhancing Technologies 2025(1) (2025)
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Web browser fingerprinting can be used to identify and track users across the Web, even without cookies, by collecting attributes from users' devices to create unique "fingerprints". This technique and resulting privacy risks have been studied for over a decade. Yet further research is limited because prior studies did not openly publish their data. Additionally, data in prior studies had biases and lacked user demographics.
Here we publish a first-of-its-kind open dataset that includes browser attributes with users' demographics, collected from 8,400 US study participants, with their informed consent. Our data collection process also conducted an experiment to study what impacts users' likelihood to share browser data for open research, in order to inform future data collection efforts, with survey responses from a total of 12,461 participants. Female participants were significantly less likely to share their browser data, as were participants who were shown the browser data we asked to collect.
In addition we demonstrate how fingerprinting risks differ across demographic groups. For example, we find lower income users are more at risk, and find that as users' age increases, they are both more likely to be concerned about fingerprinting and at real risk of fingerprinting. Furthermore, we demonstrate an overlooked risk: user demographics, such as gender, age, income level, ethnicity and race, can be inferred from browser attributes commonly used for fingerprinting, and we identify which browser attributes most contribute to this risk.
Overall, we show the important role of user demographics in the ongoing work that intends to assess fingerprinting risks and improve user privacy, with findings to inform future privacy enhancing browser developments. The dataset and data collection tool we openly publish can be used to further study research questions not addressed in this work.
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Improved FPT Approximation Scheme and Approximate Kernel for Biclique-Free Max k-Weight SAT: Greedy Strikes Back
Theoretical Computer Science, 1028 (2025)
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In the Max k-Weight SAT (aka Max SAT with Cardinality Constraint) problem, we are given a CNF formula with n variables and m clauses together with a positive integer k. The goal is to find an assignment where at most k variables are set to one that satisfies as many constraints as possible. Recently, Jain et al. (SODA 2023) gave an FPT approximation scheme (FPT-AS) with running time 2^O((dk/ε)^d) * (n + m)^O(1) for Max k-Weight SAT when the incidence graph is K_{d,d}-free. They asked whether a polynomial-size approximate kernel exists. In this work, we answer this question positively by giving an (1 − ε)-approximate kernel with (dk/ε)^O(d) variables. This also implies an improved FPT-AS with running time (dk/ε)^O(dk) * (n+m)^O(1)-time algorithm for the problem. Our approximate kernel is based mainly on a couple of greedy strategies together with a sunflower lemma-style reduction rule.
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Differentially Private Insights into AI Use
Daogao Liu
Pritish Kamath
Alexander Knop
Adam Sealfon
Da Yu
Chiyuan Zhang
Conference on Language Modeling (COLM) 2025 (2025)
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We introduce Urania, a novel framework for generating insights about LLM chatbot interactions with rigorous differential privacy (DP) guarantees. The framework employs a private clustering mechanism and innovative keyword extraction methods, including frequency-based, TF-IDF-based, and LLM-guided approaches. By leveraging DP tools such as clustering, partition selection, and histogram-based summarization, Urania provides end-to-end privacy protection. Our evaluation assesses lexical and semantic content preservation, pair similarity, and LLM-based metrics, benchmarking against a non-private method inspired by CLIO (Tamkin et al., 2024). Moreover, we develop a simple empirical privacy evaluation that demonstrates the enhanced robustness of our DP pipeline. The results show the framework’s ability to extract meaningful conversational insights while maintaining stringent user privacy, effectively balancing data utility with privacy preservation.
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When dividing items among agents, two of the most widely studied fairness notions are envy-freeness and proportionality. We consider a setting where m chores are allocated to n agents and the disutility of each chore for each agent is drawn from a probability distribution. We show that an envy-free allocation exists with high probability provided that m ≥ 2n, and moreover, m must be at least n + Θ(n) in order for the existence to hold.
On the other hand, we prove that a proportional allocation is likely to exist as long as m = ω(1), and this threshold is asymptotically tight. Our results reveal a clear contrast with the allocation of goods, where a larger number of items is necessary to ensure existence for both notions.
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PREM: Privately Answering Statistical Queries with Relative Error
Sushant Sachdeva
Cristóbal Guzmán
Alexander Knop
Pritish Kamath
COLT (2025)
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We introduce PREM (Private Relative Error Multiplicative weight update) a new (ε, δ)-DP mechanism for privately generating synthetic data that achieves a relative error guarantee for linear queries. Namely, for a domain X, a family F of queries f : X → {0, 1}, and ζ > 0, the mechanism on input dataset D ∈ X^n outputs a synthetic dataset D ̃ ∈ X^n such that all linear queries in F on D, namely sum_x∈D f(x) for f ∈ F, are within a 1 ± ζ multiplicative factor of the corresponding value on D ̃ up to an additive error that is polynomial in log |F|, log |X |, log n, log(1/δ), 1/ε, and 1/ζ. This is in contrast to the standard additive-error only setting considered in the literature, which is known to require polynomial error in at least one of n, |F|, or |X |. We complement the algorithm with nearly matching lower bounds.
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