Related papers: Algebraic constructions of efficient broadcast net…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
It is known that the number of vertices of a graph of diameter two cannot exceed $d^2+1$. In this contribution we give a new lower bound for orders of Cayley graphs of diameter two in the form $C(d,2)>0.684d^2$ valid for all degrees $d\geq…
We consider the problem of clustering graph nodes over large-scale dynamic graphs, such as citation networks, images and web networks, when graph updates such as node/edge insertions/deletions are observed distributively. We propose…
We present a simple mechanism, which can be randomised, for constructing sparse $3$-uniform hypergraphs with strong expansion properties. These hypergraphs are constructed using Cayley graphs over $\mathbb{Z}_2^t$ and have vertex degree…
In wireless networks, consisting of battery-powered devices, energy is a costly resource and most of it is spent on transmitting and receiving messages. Broadcast is a problem where a message needs to be transmitted from one node to all…
In this article, we propose a growing network model based on an optimal policy involving both topological and geographical measures. In this model, at each time step, a new node, having randomly assigned coordinates in a $1 \times 1$…
Communication networks are important infrastructures in contemporary society. There are still many challenges that are not fully solved and new solutions are proposed continuously in this active research area. In recent years, to model the…
Consider the broadcast relay channel (BRC) which consists of a source sending information over a two user broadcast channel in presence of two relay nodes that help the transmission to the destinations. Clearly, this network with five nodes…
We employ the mathematical programming approach in conjunction with the graph theory to study the structure of correspondent banking networks. Optimizing the network requires decisions to be made to onboard, terminate or restrict the bank…
In this paper, we study lower bounds for randomized solutions to the maximal independent set (MIS) and connected dominating set (CDS) problems in the dual graph model of radio networks---a generalization of the standard graph-based model…
The problem of finding the largest connected subgraph of a given undirected host graph, subject to constraints on the maximum degree $\Delta$ and the diameter $D$, was introduced in \cite{maxddbs}, as a generalization of the Degree-Diameter…
A bound on the maximum information transmission rate through a cascade of Gaussian links is presented. The network model consists of a source node attempting to send a message drawn from a finite alphabet to a sink, through a cascade of…
Motivated by very large-scale communication networks, we newly introduce exponentiation of graphs. Using the exponential operation on graphs, we can construct various graphs of multi-exponential order with logarithmic diameter. We show that…
We consider a network of nodes distributed in physical space without physical links communicating through message broadcasting over specified distances. Typically, communication using smaller distances is desirable due to savings in energy…
In this work we consider the HYBRID model of distributed computing, introduced recently by Augustine, Hinnenthal, Kuhn, Scheideler, and Schneider (SODA 2020), where nodes have access to two different communication modes: high-bandwidth…
We define a range of new coarse geometric invariants based on various graph-theoretic measures of complexity for finite graphs, including: treewidth, pathwidth, cutwidth and bandwidth. We prove that, for bounded degree graphs, these…
We study the problem of learning the structure of an optimal Bayesian network when additional constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the network or its moralized graph…
This paper concerns all-to-all network routing on regular digraphs. In previous work we focused on efficient routing in highly symmetric digraphs with low diameter for fixed degree. Here, we show that every connected regular digraph has an…
We propose a new \cu{class-optimal} algorithm for the distributed computation of Wasserstein Barycenters over networks. Assuming that each node in a graph has a probability distribution, we prove that every node can reach the barycenter of…
The local broadcast problem assumes that processes in a wireless network are provided messages, one by one, that must be delivered to their neighbors. In this paper, we prove tight bounds for this problem in two well-studied wireless…