Research
Research
Research
Research
184+ open-access research outputs.
Since the breakthrough superpolynomial multilinear formula lower bounds of Raz (Theory of Computing 2006), proving such lower bounds against multilinear algebraic branching programs (mABPs) has been a…
The $k$-means problem is a classic objective for modeling clustering in a metric space. Given a set of points in a metric space, the goal is to find $k$ representative points so as to minimize the sum…
Locally decodable codes (LDCs) are error correction codes that allow recovery of any single message symbol by probing only a small number of positions from the (possibly corrupted) codeword. Relaxed l…
The Spearman footrule is a voting rule that takes as input voter preferences expressed as rankings. It outputs a ranking that minimizes the sum of the absolute differences between the position of each…
This paper investigates the semi-streaming complexity of \textit{$k$-partial coloring}, a generalization of proper graph coloring. For $k \geq 1$, a $k$-partial coloring requires that each vertex $v$ …
Deploying large language models (LLMs) on heterogeneous edge devices demands frameworks that jointly optimize energy efficiency, inference quality, and reliability. Our prior QEIL v1 (Kumar & Jha, 202…
The Courtade-Kumar conjecture posits that dictatorship functions maximize the mutual information between the function's output and a noisy version of its input over the Boolean hypercube. We present t…
In Bayesian single-item auctions, a monotone bidding strategy--one that prescribes a higher bid for a higher value type--can be equivalently represented as a partition of the quantile space into conse…
A recent work of Goyal, Harsha, Kumar and Shankar gave nearly linear time algorithms for the list decoding of Folded Reed-Solomon codes (FRS) and univariate multiplicity codes up to list decoding capa…
Graphical user interfaces (GUIs) are the primary medium for human-computer interaction, yet automating GUI interactions remains challenging due to the complexity of visual elements, dynamic environmen…
We first extend the results of Chatterjee,Kumar,Shi,Volk(Computational Complexity 2022) by showing that the degree $d$ elementary symmetric polynomials in $n$ variables have formula lower bounds of $\…
Clustering is a fundamental technique in data analysis, with the $k$-means being one of the widely studied objectives due to its simplicity and broad applicability. In many practical scenarios, data p…
Virtual Reality (VR) is often described as the "ultimate empathy machine," framing disability as an experience to be simulated through such technologies, which can reduce disability to a spectacle of …
In the $k$-Edge Connected Spanning Subgraph ($k$-ECSS) problem we are given a (multi-)graph $G=(V,E)$ with edge costs and an integer $k$, and seek a min-cost $k$-edge-connected spanning subgraph of $G…
We show that the GCD of two univariate polynomials can be computed by (piece-wise) algebraic circuits of constant depth and polynomial size over any sufficiently large field, regardless of the charact…
We show that algebraic formulas and constant-depth circuits are closed under taking factors. In other words, we show that if a multivariate polynomial over a field of characteristic zero has a small c…
We present an algorithm for simulating a distribution using prefix conditional samples (Adar, Fischer and Levi, 2024), as well as ``prefix-compatible'' conditional models such as the interval model (C…
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 …
Given a sequence of $N$ independent sources $\mathbf{X}_1,\mathbf{X}_2,\dots,\mathbf{X}_N\sim\{0,1\}^n$, how many of them must be good (i.e., contain some min-entropy) in order to extract a uniformly …
The Steiner Forest problem, also known as the Generalized Steiner Tree problem, is a fundamental optimization problem on edge-weighted graphs where, given a set of vertex pairs, the goal is to select …
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