English
Related papers

Related papers: Low-Degree Testing Over Grids

200 papers

We give two new characterizations of ($\F_2$-linear) locally testable error-correcting codes in terms of Cayley graphs over $\F_2^h$: \begin{enumerate} \item A locally testable code is equivalent to a Cayley graph over $\F_2^h$ whose set of…

Computational Complexity · Computer Science 2013-08-26 Parikshit Gopalan , Salil Vadhan , Yuan Zhou

For an increasing monotone graph property $\mP$ the \emph{local resilience} of a graph $G$ with respect to $\mP$ is the minimal $r$ for which there exists of a subgraph $H\subseteq G$ with all degrees at most $r$ such that the removal of…

Combinatorics · Mathematics 2011-02-01 Sonny Ben-Shimon , Michael Krivelevich , Benny Sudakov

We study data-driven least squares (LS) problems with semidefinite (SD) constraints and derive finite-sample guarantees on the spectrum of their optimal solutions when these constraints are relaxed. In particular, we provide a high…

Systems and Control · Electrical Eng. & Systems 2026-02-11 Filippo Fabiani , Andrea Simonetto

We consider the problem of $L_p$-testing of class of bounded derivative properties over hypergrid domain with points distributed according to some product distribution. This class includes monotonicity, the Lipschitz property,…

Data Structures and Algorithms · Computer Science 2014-05-02 Kashyap Dixit

Group testing is concerned with identifying $t$ defective items in a set of $m$ items, where each test reports whether a specific subset of items contains at least one defective. In non-adaptive group testing, the subsets to be tested are…

Computational Geometry · Computer Science 2020-12-03 Benjamin Aram Berendsohn , László Kozma

We study property testing of (di)graph properties in bounded-degree graph models. The study of graph properties in bounded-degree models is one of the focal directions of research in property testing in the last 15 years. However, despite…

Computational Complexity · Computer Science 2020-11-03 Hiro Ito , Areej Khoury , Ilan Newman

The aim of this paper is to give a new proof that any very weak $s$-harmonic function $u$ in the unit ball $B$ is smooth. As a first step, we improve the local summability properties of $u$. Then, we exploit a suitable version of the…

Analysis of PDEs · Mathematics 2024-12-05 Alessandro Carbotti , Simone Cito , Domenico Angelo La Manna , Diego Pallara

Property Testing is a formal framework to study the computational power and complexity of sampling from combinatorial objects. A central goal in standard graph property testing is to understand which graph properties are testable with…

Data Structures and Algorithms · Computer Science 2025-09-08 Artur Czumaj , Christian Sohler , Stefan Walzer

Empirical researchers often use slope-homogeneity tests to assess whether slopes can be treated as common across units. A key difficulty is that heterogeneity may be concentrated in a small number of units, so that a failure to reject…

Econometrics · Economics 2026-04-16 Antonio Raiola , Nazarii Salish

This paper is a journal counterpart to our FOCS 2021 paper, in which we initiate the study of property testing problems concerning a finite system of relations $E$ between permutations, generalizing the study of stability in permutations.…

Group Theory · Mathematics 2024-07-11 Oren Becker , Alexander Lubotzky , Jonathan Mosheiff

We show that if the degree sequence of a graph $G$ is close in $\ell_1$-distance to a given realizable degree sequence $(d_1,\dots,d_n)$, then $G$ is close in edit distance to a graph with degree sequence $(d_1,\dots,d_n)$. We then use this…

Combinatorics · Mathematics 2020-09-29 Lior Gishboliner

Given a family $X$ of subsets of $[n]$ and an ensemble of local functions $\{f_s:s\to\Sigma\; | \; s\in X\}$, an agreement test is a randomized property tester that is supposed to test whether there is some global function $G:[n]\to\Sigma$…

Computational Complexity · Computer Science 2024-04-15 Yotam Dikstein , Irit Dinur

Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…

Optimization and Control · Mathematics 2024-12-19 Andrey Sadchikov , Savelii Chezhegov , Aleksandr Beznosikov , Alexander Gasnikov

We give a distributed algorithm in the {\sf CONGEST} model for property testing of planarity with one-sided error in general (unbounded-degree) graphs. Following Censor-Hillel et al. (DISC 2016), who recently initiated the study of property…

Distributed, Parallel, and Cluster Computing · Computer Science 2019-08-15 Reut Levi , Moti Medina , Dana Ron

The locality of a graph problem is the smallest distance $T$ such that each node can choose its own part of the solution based on its radius-$T$ neighborhood. In many settings, a graph problem can be solved efficiently with a distributed or…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-12-14 Yi-Jun Chang , Jan Studený , Jukka Suomela

This paper deals with unit root issues in time series analysis. It has been known for a long time that unit root tests may be flawed when a series although stationary has a root close to unity. That motivated recent papers dedicated to…

Statistics Theory · Mathematics 2024-06-04 Marie Badreau , Frédéric Proïa

We consider the well-known method of least squares on an equidistant grid with $N+1$ nodes on the interval $[-1,1]$ with the goal to approximate a function $f\in\mathcal{C}\left[-1,1\right]$ by a polynomial of degree $n$. We investigate the…

Numerical Analysis · Mathematics 2025-10-20 René Goertz

A polynomial identity testing algorithm must determine whether an input polynomial (given for instance by an arithmetic circuit) is identically equal to 0. In this paper, we show that a deterministic black-box identity testing algorithm for…

Computational Complexity · Computer Science 2010-08-02 Pascal Koiran

We propose a goodness-of-fit test for degree-corrected stochastic block models (DCSBM). The test is based on an adjusted chi-square statistic for measuring equality of means among groups of $n$ multinomial distributions with $d_1,\dots,d_n$…

Statistics Theory · Mathematics 2022-09-23 Linfan Zhang , Arash A. Amini

The study of Locally Checkable Labelings (LCLs) has led to a remarkably precise characterization of the distributed time complexities that can occur on bounded-degree trees. A central feature of this complexity landscape is the existence of…

Distributed, Parallel, and Cluster Computing · Computer Science 2026-02-17 Gustav Schmid