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Optimization decomposition methods are a fundamental tool to develop distributed solution algorithms for large scale optimization problems arising in fields such as machine learning and optimal control. In this paper, we present an…

Among the novel metrics used to study the relative importance of nodes in complex networks, k-core decomposition has found a number of applications in areas as diverse as sociology, proteinomics, graph visualization, and distributed system…

Many combinatorial optimization problems can be approximated within $(1 \pm \epsilon)$ factors in $\text{poly}(\log n, 1/\epsilon)$ rounds in the LOCAL model via network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018]. These approaches…

This paper considers the network slicing (NS) problem which attempts to map multiple customized virtual network requests to a common shared network infrastructure and allocate network resources to meet diverse service requirements. This…

We study the problem of computing a minimal subset of nodes of a given asynchronous Boolean network that need to be controlled to drive its dynamics from an initial steady state (or attractor) to a target steady state. Due to the phenomenon…

Pseudospectral analysis is fundamental for quantifying the sensitivity and transient behavior of nonnormal matrices, yet its computational cost scales cubically with dimension, rendering it prohibitive for large-scale systems. While…

We extend the decomposition approach for learning Bayesian networks (BNs) proposed by (Xie et. al.) to learning multivariate regression chain graphs (MVR CGs), which include BNs as a special case. The same advantages of this decomposition…

We present a novel distributed computing framework that is robust to slow compute nodes, and is capable of both approximate and exact computation of linear operations. The proposed mechanism integrates the concepts of randomized sketching…

We use the k-core decomposition to visualize large scale complex networks in two dimensions. This decomposition, based on a recursive pruning of the least connected vertices, allows to disentangle the hierarchical structure of networks by…

This work introduces a highly scalable spectral graph densification framework for learning resistor networks with linear measurements, such as node voltages and currents. We prove that given $O(\log N)$ pairs of voltage and current…

A useful approach to the mathematical analysis of large-scale biological networks is based upon their decompositions into monotone dynamical systems. This paper deals with two computational problems associated to finding decompositions…

Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of…

Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…

Balanced partitioning is often a crucial first step in solving large-scale graph optimization problems, e.g., in some cases, a big graph can be chopped into pieces that fit on one machine to be processed independently before stitching the…

We propose a new scalable method to optimize the architecture of an artificial neural network. The proposed algorithm, called Greedy Search for Neural Network Architecture, aims to determine a neural network with minimal number of layers…

Transmission line failures in power systems propagate and cascade non-locally. This well-known yet counter-intuitive feature makes it even more challenging to optimally and reliably operate these complex networks. In this work we present a…

Interconnected networks have been shown to be much more vulnerable to random and targeted failures than isolated ones, raising several interesting questions regarding the identification and mitigation of their risk. The paradigm to address…

Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to…

The connectivity structure of a network can be very sensitive to removal of certain nodes in the network. In this paper, we study the sensitivity of the largest component size to node removals. We prove that minimizing the largest component…

Graphs, consisting of vertices and edges, are vital for representing complex relationships in fields like social networks, finance, and blockchain. Visualizing these graphs helps analysts identify structural patterns, with readability…