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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…
Distributed Graph Neural Network (GNN) training suffers from substantial communication overhead due to the inherent neighborhood dependency in graph-structured data. This neighbor explosion problem requires workers to frequently exchange…
A unified approach to studying convergence and stochastic stability of continuous time consensus protocols (CPs) is presented in this work. Our method applies to networks with directed information flow; both cooperative and noncooperative…
This work investigates fault-resilient federated learning when the data samples are non-uniformly distributed across workers, and the number of faulty workers is unknown to the central server. In the presence of adversarially faulty workers…
Let Delta>1 be a fixed integer. We show that the random graph G(n,p) with p>>(log n/n)^{1/Delta} is robust with respect to the containment of almost spanning bipartite graphs H with maximum degree Delta and sublinear bandwidth in the…
In this paper, we showcase the interplay between discrete and continuous optimization in network-structured settings. We propose the first fully decentralized optimization method for a wide class of non-convex objective functions that…
Graph Convolutional Networks (GCNs) are extensively utilized for deep learning on graphs. The large data sizes of graphs and their vertex features make scalable training algorithms and distributed memory systems necessary. Since the…
Distributed linear algebraic equation over networks, where nodes hold a part of problem data and cooperatively solve the equation via node-to-node communications, is a basic distributed computation task receiving an increasing research…
Tolerance against failures and errors is an important feature of many complex networked systems [1,2]. It has been shown that a class of inhomogeneously wired networks called scale-free[1,3] networks can be surprisingly robust to failures,…
A networked system can be made resilient against adversaries and attacks if the underlying network graph is structurally robust. For instance, to achieve distributed consensus in the presence of adversaries, the underlying network graph…
Compression and sparsification algorithms are frequently applied in a preprocessing step before analyzing or optimizing large networks/graphs. In this paper we propose and study a new framework contracting edges of a graph (merging vertices…
We propose the CLEX supercomputer topology and routing scheme. We prove that CLEX can utilize a constant fraction of the total bandwidth for point-to-point communication, at delays proportional to the sum of the number of intermediate hops…
We study sparse linear regression over a network of agents, modeled as an undirected graph and no server node. The estimation of the $s$-sparse parameter is formulated as a constrained LASSO problem wherein each agent owns a subset of the…
The study of fault-tolerant data structures for various network design problems is a prominent area of research in computer science. Likewise, the study of NP-Complete problems lies at the heart of computer science with numerous results in…
Many complex systems, such as communication networks, display a surprising degree of robustness: while key components regularly malfunction, local failures rarely lead to the loss of the global information-carrying ability of the network.…
In this paper, we investigate the approximate consensus problem in highly dynamic networks in which topology may change continually and unpredictably. We prove that in both synchronous and partially synchronous systems, approximate…
We address the problem of distributed state estimation of a linear dynamical process in an attack-prone environment. Recent attempts to solve this problem impose stringent redundancy requirements on the measurement and communication…
Neural diffusion on graphs is a novel class of graph neural networks that has attracted increasing attention recently. The capability of graph neural partial differential equations (PDEs) in addressing common hurdles of graph neural…
We study the problem of constrained distributed optimization in multi-agent networks when some of the computing agents may be faulty. In this problem, the system goal is to have all the non-faulty agents collectively minimize a global…
Graph connectivity is a fundamental combinatorial optimization problem that arises in many practical applications, where usually a spanning subgraph of a network is used for its operation. However, in the real world, links may fail…