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Given a network of fixed size $n$ and an initial distribution of data, we derive sufficient connectivity conditions on a sequence of time-varying digraphs for (a) data collection and (b) data dissemination, within at most $(n-1)$…
We present a streaming algorithm for the vertex connectivity problem in dynamic streams with a (nearly) optimal space bound: for any $n$-vertex graph $G$ and any integer $k \geq 1$, our algorithm with high probability outputs whether or not…
We define the Streaming Communication model that combines the main aspects of communication complexity and streaming. We consider two agents that want to compute some function that depends on inputs that are distributed to each agent. The…
Information dissemination is a fundamental problem in parallel and distributed computing. In its simplest variant, the broadcasting problem, a message has to be spread among all nodes of a graph. A prominent communication protocol for this…
In the distributed subgraph-freeness problem, we are given a graph $H$, and asked to determine whether the network graph contains $H$ as a subgraph or not. Subgraph-freeness is an extremely local problem: if the network had no bandwidth…
The network coloring game has been proposed in the literature of social sciences as a model for conflict-resolution circumstances. The players of the game are the vertices of a graph with $n$ vertices and maximum degree $\Delta$. The game…
In multi-agent systems, strong connectivity of the communication network is often crucial for establishing consensus protocols, which underpin numerous applications in decision-making and distributed optimization. However, this connectivity…
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…
In this work we address the question of efficiency of distributed computing in anonymous, congested and highly dynamic and not-always-connected networks/systems. More precisely, the system consists of an unknown number of anonymous nodes…
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…
In this work, we introduce an online model for communication complexity. Analogous to how online algorithms receive their input piece-by-piece, our model presents one of the players, Bob, his input piece-by-piece, and has the players Alice…
We study graph connectivity problem in MPC model. On an undirected graph with $n$ nodes and $m$ edges, $O(\log n)$ round connectivity algorithms have been known for over 35 years. However, no algorithms with better complexity bounds were…
The main paradigm of smoothed analysis on graphs suggests that for any large graph $G$ in a certain class of graphs, perturbing slightly the edges of $G$ at random (usually adding few random edges to $G$) typically results in a graph having…
Graph learning is often a necessary step in processing or representing structured data, when the underlying graph is not given explicitly. Graph learning is generally performed centrally with a full knowledge of the graph signals, namely…
The aim of this work is to develop a fully-distributed algorithmic framework for training graph convolutional networks (GCNs). The proposed method is able to exploit the meaningful relational structure of the input data, which are collected…
In this paper we prove lower bounds on randomized multiparty communication complexity, both in the \emph{blackboard model} (where each message is written on a blackboard for all players to see) and (mainly) in the \emph{message-passing…
Graph Neural Networks learn on graph-structured data by iteratively aggregating local neighborhood information. While this local message passing paradigm imparts a powerful inductive bias and exploits graph sparsity, it also yields three…
In this paper, we consider the question of computing sparse subgraphs for any input directed graph $G=(V,E)$ on $n$ vertices and $m$ edges, that preserves reachability and/or strong connectivity structures. We show $O(n+\min\{|{\cal…
This paper studies distributed stochastic approximation algorithms based on broadcast gossip on communication networks represented by digraphs. Weak convergence of these algorithms is proved, and an associated ordinary differential equation…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…