Related papers: Wireless Expanders
Our work in this paper is inspired by a statistical observation that is both elementary and broadly relevant to network analysis in practice -- that the uncertainty in approximating some true network graph $G=(V,E)$ by some estimated graph…
The widespread use of wireless technologies leads to an ever-increasing number of users and permanently functioning devices. However, the growth of the number of wireless users in a limited space and a limited frequency range leads to an…
A matrix-weighted graph is an undirected graph with a $k\times k$ positive semidefinite matrix assigned to each edge. There are natural generalizations of the Laplacian and adjacency matrices for such graphs. These matrices can be used to…
We obtain improved lower bounds for additive spanners, additive emulators, and diameter-reducing shortcut sets. Spanners and emulators are sparse graphs that approximately preserve the distances of a given graph. A shortcut set is a set of…
Word-representable graphs are a subset of graphs that may be represented by a word $w$ over an alphabet composed of the vertices in the graph. In such graphs, an edge exists if and only if the occurrences of the corresponding vertices…
We study two classes of extension problems, and their interconnections: (i) Extension of positive definite (p.d.) continuous functions defined on subsets in locally compact groups $G$; (ii) In case of Lie groups, representations of the…
The fault tolerance of random graphs with unbounded degrees with respect to connectivity is investigated, which relates to the reliability of wireless sensor networks with unreliable relay nodes. The model evaluates the network breakdown…
Given an undirected unweighted graph $G = (V, E)$ on $n$ vertices and $m$ edges, a subgraph $H\subseteq G$ is a spanner of $G$ with stretch function $f: \mathbb{R}_+ \rightarrow \mathbb{R}_+$, if for every pair $s, t$ of vertices in $V$,…
We propose a simple growing model for the evolution of small-world networks. It is introduced as a modified BA model in which all the edges connected to the new nodes are made locally to the creator and its nearest neighbors. It is found…
Let $G$ be a finite group, and let ${\rm{cd}}(G)$ denote the set of degrees of the irreducible complex characters of $G$. The degree graph $\Delta(G)$ of $G$ is defined as the simple undirected graph whose vertex set ${\rm{V}}(G)$ consists…
In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which…
Many analytic results for the connectivity, coverage, and capacity of wireless networks have been reported for the case where the number of nodes, $n$, tends to infinity (large-scale networks). The majority of these results have not been…
We prove that every graph of rankwidth at least $72r$ contains an induced subgraph whose minimum balanced cutrank is at least $r$, which implies a vertex subset where every balanced separation has $\mathbb{F}_2$-cutrank at least $r$. This…
Wireless communication applications has acquired a vastly increasing range over the past decade. This rapidly increasing demand implies limitations on utilizing wireless resources. One of the most important resources in wireless…
The "slope-number" of a graph $G$ is the minimum number of distinct edge slopes in a straight-line drawing of $G$ in the plane. We prove that for $\Delta\geq5$ and all large $n$, there is a $\Delta$-regular $n$-vertex graph with…
We show that some classical results on expander graphs imply growth results on normal subsets in finite simple groups. As one application, it is shown that given a nontrivial normal subset $ A $ of a finite simple group $ G $ of Lie type of…
A $t$-spanner of an undirected $n$-vertex graph $G$ is a sparse subgraph $H$ of $G$ that preserves all pairwise distances between its vertices to within multiplicative factor $t$, also called the \emph{stretch}. We investigate the problem…
In this paper we show lower bounds for a certain large class of algorithms solving the Graph Isomorphism problem, even on expander graph instances. Spielman [25] shows an algorithm for isomorphism of strongly regular expander graphs that…
Expander decompositions of graphs have significantly advanced the understanding of many classical graph problems and led to numerous fundamental theoretical results. However, their adoption in practice has been hindered due to their…
The paper considers some new properties of the so-called $A$-maximal numerical range of operators, denoted by $W_{\max}^A(\cdot)$, where $A$ is a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Some…