Pasin Manurangsi
Research Areas
Authored Publications
Sort By
Preview abstract
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.
View details
Preview abstract
A common problem in private data analysis is the partition selection problem, where each user holds a set of partitions (e.g. keys in a GROUP BY operation) from a possibly unbounded set. The challenge here is in maximizing the set of released partitions while respecting a differential privacy constraint. Previous work [DVGM21] presented an optimal (ε, δ)-DP algorithm when each user submits only a single partition. We generalize this approach to find the optimal algorithm under δ-approximate (α, ε)-R´enyi differential privacy (RDP), which allows much tighter analysis under composition. Motivated by the non-existence of a general optimality result in the case where users submit multiple partitions each, we present a simple extension of our optimal algorithm tuned for L2 bounded weighted partition selection which can be used as a drop-in improvement over the Gaussian mechanism any time the partition frequency is not also needed. We show that our primitive can be easily plugged into state of the art partition selection algorithms (PolicyGaussian from [GGK+20] and MAD2R from [CCAEZ25]), improving performance both for parallel and sequential algorithms. Finally, we show that there is an inherent cost to algorithm which do support releasing the frequency as well as the partitions. Specifically, we formulate a basic notion of optimal approximate RDP algorithm for partition selection using additive noise, and show that there is a numerical separation between additive and non-additive noise mechanisms for this problem.
View details
Preview abstract
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.
View details
Preview abstract
Steinke [Ste25] 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? In this short note, we resolve this question positively. In particular, for a candidate set Y, we achieve error guarantee of O ̃ (log |Y|), which is within a factor of (log log |Y|)^O(1) of the exponential mechanism [MT07]. This improves on Steinke’s mechanism which achieves an error of O(log^{3/2} |Y|).
View details
Preview abstract
We study the problem of generating synthetic data under differential privacy. We establish fixed-parameter tractability (FPT) for this problem where the parameter is the treewidth of the query family’s incidence graph. Our algorithms attain optimal error rates across all regimes and are realized by two different approaches: the first is based on linear programming (LP) and the FPT of the separation problem for the LP dual; the second is based on a subsampled private multiplicative weights method, where we obtain FPT for sampling from Gibbs distributions. Both approaches are unified by a dynamic programming framework over a tree decomposition.
View details
Preview abstract
We study the computational cost of differential privacy in terms of memory
efficiency. While the trade-off between accuracy and differential privacy is
well-understood, the inherent cost of privacy regarding memory use remains
largely unexplored. This paper establishes for the first time an unconditional
space lower bound for user-level differential privacy by introducing a novel
proof technique based on a multi-player communication game.
Central to our approach, this game formally links the hardness of low-memory
private algorithms to the necessity of ``contribution capping''---tracking and
limiting the users who disproportionately impact the dataset. We demonstrate
that winning this communication game requires transmitting information
proportional to the number of over-active users, which translates directly to
memory lower bounds.
We apply this framework, as an example, to the fundamental problem of
estimating the number of distinct elements in a stream and we prove that any
private algorithm requires almost $\widetilde{\Omega}(T^{1/3})$ space to
achieve certain error rates in a promise variant of the problem. This resolves
an open problem in the literature (by Jain et al. NeurIPS 2023 and Cummings et
al. ICML 2025) and establishes the first exponential separation between the
space complexity of private algorithms and their non-private $\widetilde{O}(1)$
counterparts for a natural statistical estimation task. Furthermore, we show
that this communication-theoretic technique generalizes to broad classes of
problems, yielding lower bounds for private medians, quantiles, and max-select.
View details
Preview abstract
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.
View details
Preview abstract
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).
View details
Preview abstract
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)}.
View details
Preview abstract
In this work, we prove computational lower bounds against differentially private (DP) coreset. Specifically, assuming the existence of one-way functions, we show that no polynomial-time $(\epsilon, 1/n^{\omega(1)})$-DP algorithm can compute $(\alpha, \beta)$-coreset for $k$-means in the $\ell_\infty$ metric for some constant $\alpha > 1$. For the Euclidean metric, we show a similar result but only for $\alpha = 1 + \Theta\left(\frac{1}{d^2}\right)$ where $d$ is the dimension.
View details
