Pasin Manurangsi
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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 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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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 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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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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VaultGemma
Lynn Chua
Prem Eruvbetine
Chiyuan Zhang
Thomas Mesnard
Borja De Balle Pigem
Daogao Liu
Amer Sinha
Pritish Kamath
Yangsibo Huang
Christopher A. Choquette-Choo
George Kaissis
Armand Joulin
Andreas Terzis
Da Yu
Ryan McKenna
Ruibo Liu
arxiv (2025)
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In this work, we present VaultGemma 1B, a model based on the Gemma family of models fully trained with differential privacy. VaultGemma 1B is 1 billion parameter pretrained model based on the Gemma 2 series of models and uses the same dataset for training. We will be releasing a tech report and the weights of this model.
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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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Balls-and-Bins Sampling for DP-SGD
Lynn Chua
Charlie Harrison
Pritish Kamath
Ethan Leeman
Amer Sinha
Chiyuan Zhang
AISTATS (2025)
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We introduce the Balls-and-Bins sampling for differentially private (DP) optimization methods such as DP-SGD. While it has been common practice to use some form of shuffling in DP-SGD implementations, privacy accounting algorithms have typically assumed that Poisson subsampling is used instead. Recent work by Chua et al. (2024) however pointed out that shuffling based DP-SGD can have a much larger privacy cost in practical regime of parameters. We show that the Balls-and-Bins sampling achieves the “best-of-both” samplers, namely, the implementation of Balls-and-Bins sampling is similar to that of Shuffling and models trained with Balls-and-Bins based DP-SGD achieve utility comparable to those trained with Shuffle based DP-SGD at the same noise multiplier, and yet, Balls-and-Bins sampling enjoys similar-or-better privacy amplification as compared to Poisson subsampling.
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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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We study the allocation of indivisible goods under conflicting constraints, represented by a graph. In this framework, vertices correspond to goods and edges correspond to conflicts between a pair of goods. Each agent is allocated an independent set in the graph. In a recent work of [Kumar et al., 2024], it was shown that a maximal EF1 allocation exists for interval graphs and two agents with monotone valuations. We significantly extend this result by establishing that a maximal EF1 allocation exists for *any graph* when the two agents have monotone valuations. To compute such an allocation, we present a polynomial-time algorithm for additive valuations as well as a pseudo-polynomial time algorithm for monotone valuations. Moreover, we complement our findings by providing a counter example demonstrating a maximal EF1 allocation may not exist for three agents with monotone valuations. Additionally, we establish NP-hardness of determining the existence of such allocations for every fixed number n of agents.
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