Related papers: Distributed Testing of Conductance
A random walk on a directed graph gives a Markov chain on the vertices of the graph. An important question that arises often in the context of Markov chain is whether the uniform distribution on the vertices of the graph is a stationary…
An $(\alpha,\beta)$-ruling set of a graph $G=(V,E)$ is a set $R\subseteq V$ such that for any node $v\in V$ there is a node $u\in R$ in distance at most $\beta$ from $v$ and such that any two nodes in $R$ are at distance at least $\alpha$…
Suppose $G$ is a graph with degrees bounded by $d$, and one needs to remove more than $\epsilon n$ of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of $G$ is far from…
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph $H$ to be colored is locally embedded within the communication graph $G$. Besides generalizing…
Random geometric graphs (RGGs) are commonly used to model networked systems that depend on the underlying spatial embedding. We concern ourselves with the probability distribution of an RGG, which is crucial for studying its random…
In this paper we initiate the study of property testing in simultaneous and non-simultaneous multi-party communication complexity, focusing on testing triangle-freeness in graphs. We consider the $\textit{coordinator}$ model, where we have…
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…
In a graph, the minimum cycle bases are a set of linearly independent cycles that can be used to represent any cycle within that cycle space of graph. These bases are useful in various contexts, including the intricate analysis of…
The sinkless orientation problem plays a key role in understanding the foundations of distributed computing. The problem can be used to separate two fundamental models of distributed graph algorithms, LOCAL and SLOCAL: the locality of…
We consider the problem of testing whether two finite-dimensional random dot product graphs have generating latent positions that are independently drawn from the same distribution, or distributions that are related via scaling or…
Let $(G,\mu)$ be a uniformly elliptic random conductance graph on $\mathbb{Z}^d$ with a Poisson point process of particles at time $t=0$ that perform independent simple random walks. We show that inside a cube $Q_K$ of side length $K$, if…
In applications of group testing in networks, e.g. identifying individuals who are infected by a disease spread over a network, exploiting correlation among network nodes provides fundamental opportunities in reducing the number of tests…
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…
A number of recent papers -- e.g. Brandt et al. (STOC 2016), Chang et al. (FOCS 2016), Ghaffari & Su (SODA 2017), Brandt et al. (PODC 2017), and Chang & Pettie (FOCS 2017) -- have advanced our understanding of one of the most fundamental…
In this paper we ask which properties of a distributed network can be computed from a little amount of local information provided by its nodes. The distributed model we consider is a restriction of the classical CONGEST (distributed) model…
The dominating set problem and its generalization, the distance-$r$ dominating set problem, are among the well-studied problems in the sequential settings. In distributed models of computation, unlike for domination, not much is known about…
Distributed property testing in networks has been introduced by Brakerski and Patt-Shamir (2011), with the objective of detecting the presence of large dense sub-networks in a distributed manner. Recently, Censor-Hillel et al. (2016) have…
Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the…
Graphs are a powerful way to model interactions and relationships in data from a wide variety of application domains. In this setting, entities represented by vertices at the "center" of the graph are often more important than those…
The mixing time of a graph is an important metric, which is not only useful in analyzing connectivity and expansion properties of the network, but also serves as a key parameter in designing efficient algorithms. We introduce a new notion…