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Dynamic Trace Estimation

A practical algorithm for solving the implicit trace estimation problem is presented and it is proved that, in a natural setting, its complexity is quadratically better than the standard solution of repeatedly applying Hutchinson's stochastic trace estimator.
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A Tight Analysis of Hutchinson's Diagonal Estimator

Let $\mathbf{A}\in \mathbb{R}^{n\times n}$ be a matrix with diagonal $\text{diag}(\mathbf{A})$ and let $\bar{\mathbf{A}}$ be $\mathbf{A}$ with its diagonal set to all zeros. We show that Hutchinson's…
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Metric Clustering and MST with Strong and Weak Distance Oracles

This model captures the increasingly common trade-off between employing both an expensive similarity model and a less accurate but cheaper model, and gives constant factor approximation algorithms with only strong oracle point queries, and proves that $\Omega(k)$ queries are required for any bounded approximation.
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Learning-augmented Maximum Independent Set

This work shows an algorithm that obtains an $\tilde{O}(\sqrt{\Delta}/\varepsilon)$-approximation in $O(m)$ time where $\Delta$ is the maximum degree of the graph.
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An Energy-Based View of Graph Neural Networks

This work considers combining graph neural networks with the energy-based view of Grathwohl et al. (2019) with the aim of obtaining a more robust classifier, and proposes a novel method to ensure generation over features as well as the adjacency matrix.
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Hardness and Approximation Algorithms for Balanced Districting Problems

NP-hardness for an approximation better than $n^{1/2-\delta}$ for any constant $\delta>0$ in general graphs even when the districts are star graphs is shown, as well as NP-hardness on complete graphs, tree graphs, planar graphs and other restricted settings.
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The Price of Privacy For Approximating Max-CSP

This work studies approximation algorithms for Maximum Constraint Satisfaction Problems (Max-CSPs) under differential privacy (DP) where the constraints are considered sensitive data and devise a polynomial-time algorithm which matches this barrier under the assumptions that the instances are bounded-degree and triangle-free.
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Fully Dynamic Adversarially Robust Correlation Clustering in Polylogarithmic Update Time

The main technical ingredient is an algorithm that maintains $\textit{sparse-dense decomposition}$ with $\text{polylog}{(n)}$ update time, which could be of independent interest.
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Integer Subspace Differential Privacy

This work proposes integer subspace differential privacy to rigorously articulate the privacy guarantee when data products maintain both the invariants and integer characteristics, and demonstrates the composition and post-processing properties of the proposal.
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Relative Error Fair Clustering in the Weak-Strong Oracle Model

This work achieves the first $(1+\varepsilon)-coresets for fair $k$-median clustering using $\text{poly}\left(\frac{k}{\varepsilon}\cdot\log n\right)$ queries to the strong oracle, and implies coresets for the standard setting (without fairness constraints).
arXiv (opens in a new tab)
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