arXiv subjects

Jabari Hastings

Publications and source records attributed to Jabari Hastings.

8 recordsLinked to original sources

arXiv2026

Stable Voting Rules on the Edge of Optimal Metric Distortion

We prove the existence of a randomized voting rule with metric distortion at most $2.13713$, within $0.025$ of the lower bound of $2.11264$. Our rule comes from a generalization of stable $k$-lotteries developed in the context of committee selection. In contrast to prior work, our rule samples from a single distribution derived from a zero-sum game, without mixing between voting rules. Our result also gives sharp distortion bounds for stable $k$-lotteries, and in particular shows that stable $2$-lotteries have distortion $7/3$, despite only relying on aggregate preferences over triples of candidates.

cs.GT↗

arXiv2026

Maximum-Cost Strategic Facility Location: The Limits of Randomization

We consider strategic facility location in Euclidean space $\mathbb R^d$, where a mechanism selects a single facility based on the reported locations of $n$ agents and seeks to minimize the maximum distance from any agent to the facility. The optimal approximation ratio of deterministic strategyproof mechanisms is $2$. Whether randomization can yield a universal constant improvement over this factor has remained a major open question. We show that for $d \geq 2$, every strategyproof-in-expectation mechanism has approximation ratio at least \[ α(\mathcal M) \ge 2 - e^{-Θ(\sqrt d)} - O\left(n^{-2/(d-1)}\right). \] Therefore, no strategyproof-in-expectation mechanism can guarantee a $(2-\varepsilon)$-approximation uniformly over all $n$ and $d$, for any universal constant $\varepsilon>0$.

cs.GT↗

arXiv2026

Strategic Facility Location with $p$-Norm Social Costs

We consider the strategic facility location problem in $\ell_q(\mathbb R^d)$ spaces where the social cost is defined by an arbitrary $p$-norm of the individual costs. While the optimal approximation ratios for deterministic strategyproof mechanisms are well established in the $d = 1$ setting, the guarantees for multi-dimensional spaces under an arbitrary $p$-norm are less understood. In this work, we analyze the well-studied, strategyproof coordinate-wise median (CM) mechanism and provide approximation guarantees for these generalized social costs. * We show that the CM mechanism is in fact robust to a broader class of social objectives: for every monotone symmetric norm objective, including all $p$-norm social costs, its approximation ratio never exceeds $3$ in arbitrary $\ell_q(\mathbb R^d)$ spaces, regardless of the dimension. * For $d = 2$, we establish tight approximation ratios for all $p, q \geq 1$ in $\ell_q(\mathbb R^2)$. In particular, we show that the CM mechanism is a $2^{1-1/\max(p,q)}$-approximation, resolving the conjecture of Goel and Hann-Caruthers (Social Choice and Welfare, 2023) in the Euclidean case and extending the guarantee to arbitrary $\ell_q$ distances. * For $d\geq 3$, we refine the dimension-independent approximation guarantee for $p$-norm social costs in $\ell_q(\mathbb R^d)$ spaces, giving upper bounds that depend on the relationship between the social-cost norm $p$ and the underlying distance norm $q$. This generalizes the recent result of Gravin and Jia (STOC, 2025) for the utilitarian social cost.

cs.GT↗

arXiv2026

Optimal Metric Distortion for Learning-Augmented Matching on the Line

We revisit the problem of matching on the line with ordinal preferences. In the classic setting, there are $n$ agents and $n$ items in a shared unknown line metric, and the goal is to find a low-cost perfect matching using only the agents' rankings of the items by distance. A mechanism has distortion $α$ if it always outputs a matching whose cost is within a factor of $α$ of the optimum, in every consistent line metric. In the learning-augmented setting, the mechanism is also supplied with a prediction that conveys additional information about the instance. The quality of this prediction is unknown, and the goal is to optimize the mechanism's distortion when the prediction is accurate (consistency), while preserving worst-case guarantees when the prediction is arbitrarily inaccurate (robustness). We propose a mechanism that takes a matching as its prediction and guarantees $1$-consistency and $3$-robustness. By recovering an optimal matching when the prediction is perfectly accurate while retaining the optimal prediction-free distortion guarantee when it is arbitrarily inaccurate, we resolve an open question of Filos-Ratsikas et al. (IJCAI, 2025).

cs.GT↗

arXiv2026

A Unified Approach to Memory-Sample Tradeoffs for Detecting Planted Structures

We present a unified framework for proving memory lower bounds for multi-pass streaming algorithms that detect planted structures. Planted structures -- such as cliques or bicliques in graphs, and sparse signals in high-dimensional data -- arise in numerous applications, and our framework yields multi-pass memory lower bounds for many such fundamental settings. We show memory lower bounds for the planted $k$-biclique detection problem in random bipartite graphs and for detecting sparse Gaussian means. We also show the first memory-sample tradeoffs for the sparse principal component analysis (PCA) problem in the spiked covariance model. For all these problems to which we apply our unified framework, we obtain bounds which are nearly tight in the low, $O(\log n)$ memory regime. We also leverage our bounds to establish new multi-pass streaming lower bounds, in the vertex arrival model, for two well-studied graph streaming problems: approximating the size of the largest biclique and approximating the maximum density of bounded-size subgraphs. To show these bounds, we study a general distinguishing problem over matrices, where the goal is to distinguish a null distribution from one that plants an outlier distribution over a random submatrix. Our analysis builds on a new distributed data processing inequality that provides sufficient conditions for memory hardness in terms of the likelihood ratio between the averaged planted and null distributions. This result generalizes the inequality of [Braverman et al., STOC 2016] and may be of independent interest. The inequality enables us to measure information cost under the null distribution -- a key step for applying subsequent direct-sum-type arguments and incorporating the multi-pass information cost framework of [Braverman et al., STOC 2024].

cs.CC↗

arXiv2025

Fair metric distortion for matching with preferences

We consider the matching problem in the metric distortion framework. There are $n$ agents and $n$ items occupying points in a shared metric space, and the goal is to design a matching mechanism that outputs a low-cost matching between the agents and items, using only agents' ordinal rankings of the candidates by distance. A mechanism has distortion $α$ if it always outputs a matching whose cost is within a factor of $α$ of the optimum, in every instance regardless of the metric space. Typically, the cost of a matching is measured in terms of the total distance between matched agents and items, but this measure can incentivize unfair outcomes where a handful of agents bear the brunt of the cost. With this in mind, we consider how the metric distortion problem changes when the cost is instead measured in terms of the maximum cost of any agent. We show that while these two notions of distortion can in general differ by a factor of $n$, the distortion of a variant of the state-of-the-art mechanism, RepMatch, actually improves from $O(n^2)$ under the sum objective to $O(n^{1.58})$ under the max objective. We also show that for any fairness objective defined by a monotone symmetric norm, this algorithm guarantees distortion $O(n^2)$.

cs.GT↗

arXiv2024

Taking a Moment for Distributional Robustness

A rich line of recent work has studied distributionally robust learning approaches that seek to learn a hypothesis that performs well, in the worst-case, on many different distributions over a population. We argue that although the most common approaches seek to minimize the worst-case loss over distributions, a more reasonable goal is to minimize the worst-case distance to the true conditional expectation of labels given each covariate. Focusing on the minmax loss objective can dramatically fail to output a solution minimizing the distance to the true conditional expectation when certain distributions contain high levels of label noise. We introduce a new min-max objective based on what is known as the adversarial moment violation and show that minimizing this objective is equivalent to minimizing the worst-case $\ell_2$-distance to the true conditional expectation if we take the adversary's strategy space to be sufficiently rich. Previous work has suggested minimizing the maximum regret over the worst-case distribution as a way to circumvent issues arising from differential noise levels. We show that in the case of square loss, minimizing the worst-case regret is also equivalent to minimizing the worst-case $\ell_2$-distance to the true conditional expectation. Although their objective and our objective both minimize the worst-case distance to the true conditional expectation, we show that our approach provides large empirical savings in computational cost in terms of the number of groups, while providing the same noise-oblivious worst-distribution guarantee as the minimax regret approach, thus making positive progress on an open question posed by Agarwal and Zhang (2022).

cs.LG↗

arXiv2021

Wedge-Lifted Codes

We define wedge-lifted codes, a variant of lifted codes, and we study their locality properties. We show that (taking the trace of) wedge-lifted codes yields binary codes with the $t$-disjoint repair property ($t$-DRGP). When $t = N^{1/2d}$, where $N$ is the block length of the code and $d \geq 2$ is any integer, our codes give improved trade-offs between redundancy and locality among binary codes.

cs.IT↗