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In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We…
With an increasing amount of observations on the dynamics of many complex systems, it is required to reveal the underlying mechanisms behind these complex dynamics, which is fundamentally important in many scientific fields such as climate,…
Consider the following "local" cut-detection problem in a directed graph: We are given a seed vertex $x$ and need to remove at most $k$ edges so that at most $\nu$ edges can be reached from $x$ (a "local" cut) or output $\bot$ to indicate…
We study an NP-hard problem motivated by energy-efficiently maintaining the connectivity of a symmetric wireless communication network: Given an edge-weighted $n$-vertex graph, find a connected spanning subgraph of minimum cost, where the…
The Renormalization Group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric…
This paper considers fully dynamic graph algorithms with both faster worst case update time and sublinear space. The fully dynamic graph connectivity problem is the following: given a graph on a fixed set of n nodes, process an online…
We consider the problem of binary string reconstruction from the multiset of its substring compositions, i.e., referred to as the substring composition multiset, first introduced and studied by Acharya et al. We introduce a new algorithm…
Social network alignment has been an important research problem for social network analysis in recent years. With the identified shared users across networks, it will provide researchers with the opportunity to achieve a more comprehensive…
Many real-world systems involve higher-order interactions and thus demand complex models such as hypergraphs. For instance, a research article could have multiple collaborating authors, and therefore the co-authorship network is best…
Network renormalization has traditionally relied on spatial adjacency-grouping nearby nodes together, but this approach fails to capture the dynamical correlations that govern system-wide behavior in scale-free networks. We present a…
We consider network design problems in which we are given a graph and seek a min-size $2$-connected subgraph that satisfies a prescribed property. $\bullet$ In the 1-Connectivity Augmentation problem the goal is to augment a connected graph…
Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints…
We study the sparse phase retrieval problem, which seeks to recover a sparse signal from a limited set of magnitude-only measurements. In contrast to prevalent sparse phase retrieval algorithms that primarily use first-order methods, we…
Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…
Reconstructing a surface from a point cloud is an underdetermined problem. We use a neural network to study and quantify this reconstruction uncertainty under a Poisson smoothness prior. Our algorithm addresses the main limitations of…
An important problem of reconstruction of diffusion network and transmission probabilities from the data has attracted a considerable attention in the past several years. A number of recent papers introduced efficient algorithms for the…
The fundamental caching problem in networks asks to find an allocation of contents to a network of caches with the aim of maximizing the cache hit rate. Despite the problem's importance to a variety of research areas -- including not only…
Reconstructing a network of dynamic systems from observational data is an active area of research. Many approaches guarantee a consistent reconstruction under the relatively strong assumption that the network dynamics is governed by…
We study recovering a 1D order from a noisy, locally sampled pairwise comparison matrix under a tight query budget. We recast the task as reconstructing a sparse, noisy line graph and present, to our knowledge, the first method that…
We present an algorithm for finding a perfect matching in a $3$-edge-connected cubic graph that intersects every $3$-edge cut in exactly one edge. Specifically, we propose an algorithm with a time complexity of $O(n \log^4 n)$, which…