Related papers: Wireless Expanders
In this paper, we study the large-scale structure of dense regular graphs. This involves the notion of robust expansion, a recent concept which has already been used successfully to settle several longstanding problems. Roughly speaking, a…
A graph $G$ is universal for a class of graphs $\mathcal{C}$, if, up to isomorphism, $G$ contains every graph in $\mathcal{C}$ as a subgraph. In 1978, Chung and Graham asked for the minimal number $s(n)$ of edges in a graph with $n$…
Given a weighted graph $G=(V,E,w)$, a partition of $V$ is $\Delta$-bounded if the diameter of each cluster is bounded by $\Delta$. A distribution over $\Delta$-bounded partitions is a $\beta$-padded decomposition if every ball of radius…
The Bandwidth Theorem of B\"ottcher, Schacht and Taraz [Mathematische Annalen 343 (1), 175-205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this…
In recent years, with the rapid enhancement of computing power, deep learning methods have been widely applied in wireless networks and achieved impressive performance. To effectively exploit the information of graph-structured data as well…
We study the interaction of WiFi and 5G cellular networks as they exploit the recently unlocked 6-GHz spectrum for unlicensed access while conforming to the constraints imposed by the incumbent users. We derive the theoretical performance…
Preservers and additive spanners are sparse (hence cheap to store) subgraphs that preserve the distances between given pairs of nodes exactly or with some small additive error, respectively. Since real-world networks are prone to failures,…
In this paper, we study the broadcast problem in wireless networks when the broadcast is helped by a labelling scheme. We focus on two variants of broadcast: broadcast without acknowledgment (i.e. the initiator of the broadcast is not…
In this paper, we discuss how to design the graph topology to reduce the communication complexity of certain algorithms for decentralized optimization. Our goal is to minimize the total communication needed to achieve a prescribed accuracy.…
The task of finding an extension to a given partial drawing of a graph while adhering to constraints on the representation has been extensively studied in the literature, with well-known results providing efficient algorithms for…
The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$-vertex graph $G$ with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)n$ contains all $n$-vertex $k$-colourable graphs $H$ with bounded maximum degree and…
In the presented paper we study the Length-Bounded Cut problem for special graph classes as well as from a parameterized-complexity viewpoint. Here, we are given a graph $G$, two vertices $s$ and $t$, and positive integers $\beta$ and…
We introduce graphical error-correcting codes, a new notion of error-correcting codes on $[q]^n$, where a code is a set of proper $q$-colorings of some fixed $n$-vertex graph $G$. We then say that a set of $M$ proper $q$-colorings of $G$…
Due to the uncontrolled and complex real-life radio propagation environments, Claude Shannon's information theory of communications describes fundamental limits to state-of-the-art 5G radio access network (RAN) capacity, with respect to…
A radio labeling of a graph $G$ is a mapping $f$ : $V(G) \rightarrow \{0, 1, 2,...\}$ such that $|f(u)-f(v)| \geq diam(G) + 1 - d(u,v)$ holds for every pair of vertices $u$ and $v$, where $diam(G)$ is the diameter of $G$ and $d(u,v)$ is the…
The conditional diameter of a connected graph $\Gamma=(V,E)$ is defined as follows: given a property ${\cal P}$ of a pair $(\Gamma_1, \Gamma_2)$ of subgraphs of $\Gamma$, the so-called \emph{conditional diameter} or ${\cal P}$-{\em…
We consider the problem of self-healing in peer-to-peer networks that are under repeated attack by an omniscient adversary. We assume that, over a sequence of rounds, an adversary either inserts a node with arbitrary connections or deletes…
When comparing new wireless technologies, it is common to consider the effect that they have on the capacity of the network (defined as the maximum number of simultaneously satisfiable links). For example, it has been shown that giving…
The Flat Wall Theorem of Robertson and Seymour states that there is some function $f$, such that for all integers $w,t>1$, every graph $G$ containing a wall of size $f(w,t)$, must contain either (i) a $K_t$-minor; or (ii) a small subset…
Classes of graphs with bounded expansion are a generalization of both proper minor closed classes and degree bounded classes. Such classes are based on a new invariant, the greatest reduced average density (grad) of G with rank r,…