Related papers: Maximizing the algebraic connectivity in multilaye…
As model sizes in machine learning continue to scale, distributed training is necessary to accommodate model weights within each device and to reduce training time. However, this comes with the expense of increased communication overhead…
This paper investigates some relationship between the algebraic connectivity and the clique number of graphs. We characterize all extremal graphs which have the maximum and minimum the algebraic connectivity among all graphs of order $n$…
We aim to learn a sparse and connected graph from sparse data, where the number of observations K can be substantially smaller than the signal dimension N for signals x in R^N, and the underlying distribution is unknown. In this severely…
We analyze the achievable rate in interference-free wireless networks with physical layer fading channels and orthogonal multiple access. As a starting point, the point-to-point channel is considered. We find the optimal physical and…
We present a novel approach for computing a variant of eigenvector centrality for multilayer networks with inter-layer constraints on node importance. Specifically, we consider a multilayer network defined by multiple edge-weighted,…
For a graph $G$, let $\lambda_2(G)$ denote its second smallest Laplacian eigenvalue. It was conjectured that $\lambda_2(G) + \lambda_2(\overline{G}) \geq 1$, where $\bar{G}$ is the complement of $G$. Here, we prove this conjecture in the…
We investigate certain structural properties of random interdependent networks. We start by studying a property known as $r$-robustness, which is a strong indicator of the ability of a network to tolerate structural perturbations and…
An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment and…
The reliable operation of large-scale electric power networks is increasingly challenging, particularly with the integration of stochastic renewable generation. In this work, we address the problem of minimizing network transients by…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
Graph connectivity and network design problems are among the most fundamental problems in combinatorial optimization. The minimum spanning tree problem, the two edge-connected spanning subgraph problem (2-ECSS) and the tree augmentation…
Partition problems in graphs are extremely important in applications, as shown in the Data science and Machine learning literature. One approach is spectral partitioning based on a Fiedler vector, i.e., an eigenvector corresponding to the…
Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the…
We develop the necessary theory in computational algebraic geometry to place Bayesian networks into the realm of algebraic statistics. We present an algebra{statistics dictionary focused on statistical modeling. In particular, we link the…
In this paper, we consider maximizing the sum-rate in the uplink of a multi-cell OFDMA network. The problem has a non-convex combinatorial structure and is known to be NP hard. Due to the inherent complexity of implementing the optimal…
A classical result in undirected wireline networks is the near optimality of routing (flow) for multiple-unicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a…
We study the allocation of indivisible items that form an undirected graph and investigate the worst-case welfare loss when requiring that each agent must receive a connected subgraph. Our focus is on both egalitarian and utilitarian…
Quantum Internetworking is a recent field that promises numerous interesting applications, many of which require the distribution of entanglement between arbitrary pairs of users. This work deals with the problem of scheduling in an…
The deterministic wireless relay network model, introduced by Avestimehr et al., has been proposed for approximating Gaussian relay networks. This model, known as the ADT network model, takes into account the broadcast nature of wireless…
Random geometric networks consist of 1) a set of nodes embedded randomly in a bounded domain $\mathcal{V} \subseteq \mathbb{R}^d$ and 2) links formed probabilistically according to a function of mutual Euclidean separation. We quantify how…