Research
Research
Research
Research
1,740+ open-access research outputs.
Under what condition is a random constraint satisfaction problem hard to refute by the sum-of-squares (SoS) algorithm? A sufficient condition is t-wise uniformity, that is, each constraint has a t-wis…
In the Independent Set Reconfiguration problem under the Token Addition/Removal rule, given a graph $G$ and two independent sets $I$ and $J$ of $G$, we want to transform $I$ into $J$ by adding and rem…
In this work we contribute to the study of the fine-grained complexity of problems parameterized by multi-clique-width, which was initiated by F\"urer [ITCS 2017] and pursued further by Chekan and Kra…
Given a connected undirected graph $G$, a spanning tree is a subgraph $T$ of $G$ such that $V(T) = V(G)$ and $T$ is a tree. A collection of $\ell$ spanning trees $T_1,\ldots,T_\ell$ is pairwise $k$-di…
Hierarchical clustering is a fundamental task in data analysis, yet for a long time it lacked a principled objective function. Dasgupta [STOC 2016] initiated a formal framework by introducing a discre…
For a nonnegative integer $r$ and a positive integer $v$ satisfying \[ \frac{r(q-1)}{2}<v<\frac{(r+1)(q-1)}{2}, \] we define the combinatorial numbers \[ A_r(v)= \begin{cases} \display…
Toxic interactions during code reviews can undermine teamwork and hinder productivity in software engineering (SE) teams. While prior studies explore toxicity detection and empirical investigation, th…
In this paper, we exhibit $\textsf{AC}^{3}$ isomorphism tests for coprime extensions $H \ltimes N$ where $H$ is elementary Abelian and $N$ is Abelian; and groups where $\text{Rad}(G) = Z(G)$ is elemen…
The growing demand for deploying Small Language Models (SLMs) on edge devices, including laptops, smartphones, and embedded platforms, has exposed fundamental inefficiencies in existing accelerators. …
Max-Cut is a classical graph-partitioning problem where given a graph $G = (V,E)$, the objective is to find a cut $(S,S^c)$ which maximizes the number of edges crossing the cut. In a seminal work, Goe…
Rendering large-scale, unbounded scenes on AR/VR-class devices is constrained by the computation, bandwidth, and storage cost of 3D Gaussian Splatting (3DGS). We propose a low-power, low-cost 3DGS har…
Toxic interactions in open-source software development harm community collaboration. To combat this, we propose ToxiShield, a realtime browser extension that identifies and detoxifies toxic code revie…
We study two conjectures posed in the analysis of Boolean functions $f : \{-1, 1\}^n \to \{-1, 1\}$, in both of which, the Majority function plays a central role: the "Majority is Least Stable" (Benja…
Inversion of a directed graph $D$ with respect to a vertex subset $Y$ is the directed graph obtained from $D$ by reversing the direction of every arc whose endpoints both lie in $Y$. More generally, t…
Literature provides several bounds for quantum local recovery, which essentially consider the number of message qudits, the distance, the length, and the locality of the involved codes. We give a fami…
Strategic model selection and reasoning settings are more effective than ensembling for optimizing automated scoring with large language models (LLMs). We examined self-consistency (intra-model majori…
We study algorithms for approximating the permanent of a random matrix when the entries are slightly biased away from zero. This question is motivated by the goal of understanding the classical comple…
We study a Bayesian binary sequential hypothesis testing problem with multiple large language models (LLMs). Each LLM $j$ has per-query cost $c_j>0$, random waiting time with mean $\mu_j>0$ and sub-Ga…
In Grochow and Qiao (SIAM J. Comput., 2021), the complexity class Tensor Isomorphism (TI) was introduced and isomorphism problems for groups, algebras, and polynomials were shown to be TI-complete. In…
Given an $H$-minor-free graph $G$ and an integer $k$, our main technical contribution is sampling in randomized polynomial time an induced subgraph $G'$ of $G$ and a tree decomposition of $G'$ of widt…
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