Related papers: Quantum Property Testing for Bounded-Degree Direct…

Using a quantum processor to embed and process classical data enables the generation of correlations between variables that are inefficient to represent through classical computation. A fundamental question is whether these correlations…

Distribution testing can be described as follows: $q$ samples are being drawn from some unknown distribution $P$ over a known domain $[n]$. After the sampling process, a decision must be made about whether $P$ holds some property, or is far…

Suppose one has access to oracles generating samples from two unknown probability distributions P and Q on some N-element set. How many samples does one need to test whether the two distributions are close or far from each other in the…

We study the question of testing structured properties (classes) of discrete distributions. Specifically, given sample access to an arbitrary distribution $D$ over $[n]$ and a property $\mathcal{P}$, the goal is to distinguish between…

Properties of Boolean functions can often be tested much faster than the functions can be learned. However, this advantage usually disappears when testers are limited to random samples of a function $f$--a natural setting for data…

The notions of bounded expansion and nowhere denseness not only offer robust and general definitions of uniform sparseness of graphs, they also describe the tractability boundary for several important algorithmic questions. In this paper we…

The problem of learning or reconstructing an unknown graph from a known family via partial-information queries arises as a mathematical model in various contexts. The most basic type of access to the graph is via \emph{edge queries}, where…

We study property testing in the subcube conditional model introduced by Bhattacharyya and Chakraborty (2017). We obtain the first equivalence test for $n$-dimensional distributions that is quasi-linear in $n$, improving the previously…

In this paper we consider the problem of testing whether a graph has bounded arboricity. The family of graphs with bounded arboricity includes, among others, bounded-degree graphs, all minor-closed graph classes (e.g. planar graphs, graphs…

The query complexity of graph properties is well-studied when queries are on edges. We investigate the same when queries are on nodes. In this setting a graph $G = (V, E)$ on $n$ vertices and a property $\mathcal{P}$ are given. A black-box…

Recent works of Alon-Shapira and R\"odl-Schacht have demonstrated that every hereditary property of undirected graphs or hypergraphs is testable with one-sided error; informally, this means that if a graph or hypergraph satisfies that…

We study unitary property testing, where a quantum algorithm is given query access to a black-box unitary and has to decide whether it satisfies some property. In addition to containing the standard quantum query complexity model (where the…

Let $H$ be a fixed graph on $n$ vertices. Let $f_H(G) = 1$ iff the input graph $G$ on $n$ vertices contains $H$ as a (not necessarily induced) subgraph. Let $\alpha_H$ denote the cardinality of a maximum independent set of $H$. In this…

We establish the first quantitative Berry-Esseen bounds for edge eigenvector statistics in random regular graphs. For any $d$-regular graph on $N$ vertices with fixed $d \geq 3$ and deterministic unit vector $\mathbf{q} \perp \mathbf{e}$,…

Let $\{D_M\}_{M\geq 0}$ be the $n$-vertex random directed graph process, where $D_0$ is the empty directed graph on $n$ vertices, and subsequent directed graphs in the sequence are obtained by the addition of a new directed edge uniformly…

Property testers are fast randomized algorithms whose task is to distinguish between inputs satisfying some predetermined property ${\cal P}$ and those that are far from satisfying it. Since these algorithms operate by inspecting a small…

We establish nearly optimal sample complexity bounds for testing the $\rho$-clique property in the dense graph model. Specifically, we show that it is possible to distinguish graphs on $n$ vertices that have a $\rho n$-clique from graphs…

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…

A common way to accelerate shortest path algorithms on graphs is the use of a bidirectional search, which simultaneously explores the graph from the start and the destination. It has been observed recently that this strategy performs…

Hamiltonian cycles in graphs were first studied in the 1850s. Since then, an impressive amount of research has been dedicated to identifying classes of graphs that allow Hamiltonian cycles, and to related questions. The corresponding…