Related papers: A characterization of one-sided error testable gra…
In a recent work (ECCC, TR18-171, 2018), we introduced models of testing graph properties in which, in addition to answers to the usual graph-queries, the tester obtains {\em random vertices drawn according to an arbitrary distribution…
We initiate the study of quantum property testing in sparse directed graphs, and more particularly in the unidirectional model, where the algorithm is allowed to query only the outgoing edges of a vertex. In the classical unidirectional…
One of the main challenges in property testing is to characterize those properties that are testable with a constant number of queries. For unordered structures such as graphs and hypergraphs this task has been mostly settled. However, for…
We study vulnerability of a uniformly distributed random graph to an attack by an adversary who aims for a global change of the distribution while being able to make only a local change in the graph. We call a graph property $A$…
In the framework of graph property testing, we study the problem of determining if a graph admits a cluster structure. We say that a graph is $(k, \phi)$-clusterable if it can be partitioned into at most $k$ parts such that each part has…
Let $G$ be an undirected, bounded degree graph with $n$ vertices. Fix a finite graph $H$, and suppose one must remove $\varepsilon n$ edges from $G$ to make it $H$-minor free (for some small constant $\varepsilon > 0$). We give an…
A \emph{locally irregular graph} is a graph whose adjacent vertices have distinct degrees. We say that a graph $G$ can be decomposed into $k$ locally irregular subgraphs if its edge set may be partitioned into $k$ subsets each of which…
A distance estimator for a graph property $\mathcal{P}$ is an algorithm that given $G$ and $\alpha, \varepsilon >0$ distinguishes between the case that $G$ is $(\alpha-\varepsilon)$-close to $\mathcal{P}$ and the case that $G$ is…
Detecting specific structures in a network has been a very active theme of research in distributed computing for at least a decade. In this paper, we start the study of subgraph detection from the perspective of local certification.…
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…
We study verification (decision) problems for graph properties in distributed networks under the locally checkable labeling framework, where nodes use labels (proofs) and local neighborhoods to decide acceptance or rejection. Our focus is…
We present new families of goodness-of-fit tests of uniformity on a full-dimensional set $W\subset\R^d$ based on statistics related to edge lengths of random geometric graphs. Asymptotic normality of these statistics is proven under the…
In this paper, we study a hypothesis test to determine the underlying directed graph structure of nodes in a network, where the nodes represent random processes and the direction of the links indicate a causal relationship between said…
We characterize the set of properties of Boolean-valued functions on a finite domain $\mathcal{X}$ that are testable with a constant number of samples. Specifically, we show that a property $\mathcal{P}$ is testable with a constant number…
The public sharing of user information opens the door for adversaries to infer private data, leading to privacy breaches and facilitating malicious activities. While numerous studies have concentrated on privacy leakage via public user…
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…
Property graphs can be used to represent heterogeneous networks with labeled (attributed) vertices and edges. Given a property graph, simulating another graph with same or greater size with the same statistical properties with respect to…
In this paper, our goal is to characterize two graph classes based on the properties of minimal vertex (edge) separators. We first present a structural characterization of graphs in which every minimal vertex separator is a stable set. We…
Learning a graph with a specific structure is essential for interpretability and identification of the relationships among data. It is well known that structured graph learning from observed samples is an NP-hard combinatorial problem. In…
We establish the conditions under which several algorithmically exploitable structural features hold for random intersection graphs, a natural model for many real-world networks where edges correspond to shared attributes. Specifically, we…