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Recently, motivated by the rapid increase of the data size in various applications, Monemizadeh [APPROX'23] and Driemel, Monemizadeh, Oh, Staals, and Woodruff [SoCG'25] studied geometric problems in the setting where the only access to the…

Computational Geometry · Computer Science 2026-03-24 T. Schibler , J. Xue , J. Zhu

We revisit the problem of property testing for convex position for point sets in $\mathbb{R}^d$. Our results draw from previous ideas of Czumaj, Sohler, and Ziegler (ESA 2000). First, the algorithm is redesigned and its analysis is revised…

Computational Geometry · Computer Science 2023-05-09 Adrian Dumitrescu

We lower bound the complexity of finding $\epsilon$-stationary points (with gradient norm at most $\epsilon$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions…

Optimization and Control · Mathematics 2022-03-01 Yossi Arjevani , Yair Carmon , John C. Duchi , Dylan J. Foster , Nathan Srebro , Blake Woodworth

We study the basic statistical problem of testing whether normally distributed $n$-dimensional data has been truncated, i.e. altered by only retaining points that lie in some unknown truncation set $S \subseteq \mathbb{R}^n$. As our main…

Data Structures and Algorithms · Computer Science 2024-11-25 Anindya De , Shivam Nadimpalli , Rocco A. Servedio

We present an adaptive tester for the unateness property of Boolean functions. Given a function $f:\{0,1\}^n \to \{0,1\}$ the tester makes $O(n \log(n)/\epsilon)$ adaptive queries to the function. The tester always accepts a unate function,…

Data Structures and Algorithms · Computer Science 2016-08-09 Subhash Khot , Igor Shinkar

In the property testing model, the task is to distinguish objects possessing some property from the objects that are far from it. One of such properties is monotonicity, when the objects are functions from one poset to another. This is an…

Computational Complexity · Computer Science 2018-05-11 Aleksandrs Belovs

We prove that any non-adaptive algorithm that tests whether an unknown Boolean function $f: \{0, 1\}^n\to \{0, 1\}$ is a $k$-junta or $\epsilon$-far from every $k$-junta must make $\widetilde{\Omega}(k^{3/2} / \epsilon)$ many queries for a…

Computational Complexity · Computer Science 2017-04-24 Xi Chen , Rocco A. Servedio , Li-Yang Tan , Erik Waingarten , Jinyu Xie

Efficiently counting or detecting defective items is a crucial task in various fields ranging from biological testing to quality control to streaming algorithms. The \emph{group testing estimation problem} concerns estimating the number of…

Data Structures and Algorithms · Computer Science 2023-12-08 Nader H. Bshouty , Tsun-Ming Cheung , Gergely Harcos , Hamed Hatami , Anthony Ostuni

We investigate distribution testing with access to non-adaptive conditional samples. In the conditional sampling model, the algorithm is given the following access to a distribution: it submits a query set $S$ to an oracle, which returns a…

Data Structures and Algorithms · Computer Science 2018-11-06 Gautam Kamath , Christos Tzamos

We study the problems of testing and learning high-dimensional discrete convex sets. The simplest high-dimensional discrete domain where convexity is a non-trivial property is the ternary hypercube, $\{-1,0,1\}^n$. The goal of this work is…

Data Structures and Algorithms · Computer Science 2023-11-21 Hadley Black , Eric Blais , Nathaniel Harms

Group testing is an approach aimed at identifying up to $d$ defective items among a total of $n$ elements. This is accomplished by examining subsets to determine if at least one defective item is present. In our study, we focus on the…

Data Structures and Algorithms · Computer Science 2023-07-12 Nader H. Bshouty , Catherine A. Haddad-Zaknoon

We introduce a novel probabilistic group testing framework, termed Poisson group testing, in which the number of defectives follows a right-truncated Poisson distribution. The Poisson model has a number of new applications, including…

Information Theory · Computer Science 2023-07-19 Amin Emad , Olgica Milenkovic

In this paper, we consider lower bounds on the query complexity for testing CSPs in the bounded-degree model. First, for any ``symmetric'' predicate $P:{0,1}^{k} \to {0,1}$ except \equ where $k\geq 3$, we show that every (randomized)…

Data Structures and Algorithms · Computer Science 2010-07-21 Yuichi Yoshida

A Boolean function $f:\{0,1\}^d \mapsto \{0,1\}$ is unate if, along each coordinate, the function is either nondecreasing or nonincreasing. In this note, we prove that any nonadaptive, one-sided error unateness tester must make…

Computational Complexity · Computer Science 2017-06-02 Roksana Baleshzar , Deeparnab Chakrabarty , Ramesh Krishnan S. Pallavoor , Sofya Raskhodnikova , C. Seshadhri

We consider the well-studied problem of learning intersections of halfspaces under the Gaussian distribution in the challenging \emph{agnostic learning} model. Recent work of Diakonikolas et al. (2021) shows that any Statistical Query (SQ)…

Machine Learning · Computer Science 2022-02-11 Daniel Hsu , Clayton Sanford , Rocco Servedio , Emmanouil-Vasileios Vlatakis-Gkaragkounis

We consider nonadaptive group testing with Bernoulli tests, where each item is placed in each test independently with some fixed probability. We give a tight threshold on the maximum number of tests required to find the defective set under…

Information Theory · Computer Science 2017-11-16 Matthew Aldridge

We study the equivalence testing problem where the goal is to determine if the given two unknown distributions on $[n]$ are equal or $\epsilon$-far in the total variation distance in the conditional sampling model (CFGM, SICOMP16; CRS,…

Data Structures and Algorithms · Computer Science 2023-08-23 Diptarka Chakraborty , Sourav Chakraborty , Gunjan Kumar

We study the problem of estimating the size of the maximum matching in the sublinear-time setting. This problem has been extensively studied, with several known upper and lower bounds. A notable result by Behnezhad (FOCS 2021) established a…

Data Structures and Algorithms · Computer Science 2026-02-17 Vihan Shah

In this paper, we consider the problem of noiseless non-adaptive probabilistic group testing, in which the goal is high-probability recovery of the defective set. We show that in the case of $n$ items among which $k$ are defective, the…

Information Theory · Computer Science 2021-07-30 Wei Heng Bay , Eric Price , Jonathan Scarlett

We consider a general model for representing and manipulating parametric curves, in which a curve is specified by a black box mapping a parameter value between 0 and 1 to a point in Euclidean d-space. In this model, we consider the…

Computational Geometry · Computer Science 2007-05-23 Ilya Baran , Erik D. Demaine