Related papers: Distributed Subgraph Detection
We study the problem of broadcasting multiple messages in the CONGEST model. In this problem, a dedicated source node $s$ possesses a set $M$ of messages with every message of size $O(\log n)$ where $n$ is the total number of nodes. The…
Let $G=(V,E)$ be a bipartite graph embedded in a plane (or $n$-holed torus). Two subgraphs of $G$ differ by a {\it $Z$-transformation} if their symmetric difference consists of the boundary edges of a single face---and if each subgraph…
We study the computational limits of the following general hypothesis testing problem. Let H=H_n be an \emph{arbitrary} undirected graph on n vertices. We study the detection task between a ``null'' Erd\H{o}s-R\'{e}nyi random graph G(n,p)…
Many distributed optimization algorithms achieve existentially-optimal running times, meaning that there exists some pathological worst-case topology on which no algorithm can do better. Still, most networks of interest allow for…
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…
We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…
Given an undirected $n$-vertex graph $G(V,E)$ and an integer $k$, let $T_k(G)$ denote the random vertex induced subgraph of $G$ generated by ordering $V$ according to a random permutation $\pi$ and including in $T_k(G)$ those vertices with…
The class of graphs that do not contain a path on $k$ nodes as an induced subgraph ($P_k$-free graphs) has rich applications in the theory of graph algorithms. This paper explores the problem of deciding $P_k$-freeness from the viewpoint of…
We consider the task of detecting a hidden bipartite subgraph in a given random graph. This is formulated as a hypothesis testing problem, under the null hypothesis, the graph is a realization of an Erd\H{o}s-R\'{e}nyi random graph over $n$…
We present the first parallel fixed-parameter algorithm for subgraph isomorphism in planar graphs, bounded-genus graphs, and, more generally, all minor-closed graphs of locally bounded treewidth. Our randomized low depth algorithm has a…
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 present an efficient…
Supervised learning on graphs is a challenging task due to the high dimensionality and inherent structural dependencies in the data, where each edge depends on a pair of vertices. Existing conventional methods are designed for standard…
Finding sparse cuts is an important tool in analyzing large-scale distributed networks such as the Internet and Peer-to-Peer networks, as well as large-scale graphs such as the web graph, online social communities, and VLSI circuits. In…
Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded-degree…
We consider the problem of counting 4-cycles ($C_4$) in an undirected graph $G$ of $n$ vertices and $m$ edges (in bipartite graphs, 4-cycles are also often referred to as $\textit{butterflies}$). Most recently, Wang et al. (2019, 2022)…
Shortest paths problems are subject to extensive studies in classic distributed models such as the CONGEST or Congested Clique. These models dictate how nodes may communicate in order to determine shortest paths in a distributed input…
Symmetry breaking problems are among the most well studied in the field of distributed computing and yet the most fundamental questions about their complexity remain open. In this paper we work in the LOCAL model (where the input graph and…
Finding connected components in a graph is a fundamental problem in graph analysis. In this work, we present a novel minimum-mapping based Contour algorithm to efficiently solve the connectivity problem. We prove that the Contour algorithm…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Given a dynamic network, where edges appear and disappear over time, we are interested in finding sets of edges that have similar temporal behavior and form a dense subgraph. Formally, we define the problem as the enumeration of the maximal…