Related papers: Reliable Spanners for Metric Spaces
It is known that any $n$-point set in the $d$-dimensional Euclidean space $\mathbb{R}^d$, for $d = O(1)$, admits: 1) a $(1+\epsilon)$-spanner with maximum degree $\tilde{O}(\epsilon^{-d+1})$ and with lightness $\tilde{O}(\epsilon^{-d})$; 2)…
A tree $t$-spanner of a graph $G$ is a spanning tree of $G$ such that the distance between pairs of vertices in the tree is at most $t$ times their distance in $G$. Deciding tree $t$-spanner admissible graphs has been proved to be tractable…
The reliability of a network is an important parameter to consider when building a network. Different characteristics of the network can become unreliable over time or from other outside forces. In a simple setting, we model a network as a…
Tree spanners approximate distances within graphs; a subtree of a graph is a tree $t$-spanner of the graph if and only if for every pair of vertices their distance in the subtree is at most $t$ times their distance in the graph. When a…
A {\em fault-tolerant} structure for a network is required to continue functioning following the failure of some of the network's edges or vertices. In this paper, we address the problem of designing a {\em fault-tolerant} additive spanner,…
We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers, which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work…
Seminal works on light spanners over the years provide spanners with optimal lightness in various graph classes, such as in general graphs, Euclidean spanners, and minor-free graphs. Three shortcomings of previous works on light spanners…
A tree $\sigma$-spanner of a positively real-weighted $n$-vertex and $m$-edge undirected graph $G$ is a spanning tree $T$ of $G$ which approximately preserves (i.e., up to a multiplicative stretch factor $\sigma$) distances in $G$. Tree…
Additive spanners are fundamental graph structures with wide applications in network design, graph sparsification, and distance approximation. In particular, a $4$-additive spanner is a subgraph that preserves all pairwise distances up to…
The fifth generation of communication technology (5G) revolutionizes mobile networks and the associated ecosystems through the integration of cross-domain networks. Network slicing is an enabling technology for 5G as it provides dynamic,…
The \textit{node reliability} of a graph $G$ is the probability that at least one node is operational and that the operational nodes can all communicate in the subgraph that they induce, given that the edges are perfectly reliable but each…
We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse…
A classic result in the study of spanners is the existence of light low-stretch spanners for Euclidean spaces. These spanners ahve arbitrary low stretch, and weight only a constant factor greater than that of the minimum spanning tree of…
Fault tolerant distance preservers (spanners) are sparse subgraphs that preserve (approximate) distances between given pairs of vertices under edge or vertex failures. So-far, these structures have been studied mainly from a centralized…
A graph spanner is a fundamental graph structure that faithfully preserves the pairwise distances in the input graph up to a small multiplicative stretch. The common objective in the computation of spanners is to achieve the best-known…
The increasing demands in security and reliability of infrastructures call for the optimal design of their embedded complex networks topologies. The following question then arises: what is the optimal layout to fulfill best all the demands?…
Finding separable certificates of stability is important for tractability of analysis methods for large-scale networked systems. In this paper we consider the question of when a nonlinear system which is contracting, i.e. all solutions are…
A central question of network science is how functional properties of systems arise from their structure. For networked dynamical systems, structure is typically quantified with network measures. A functional property that is of theoretical…
The resiliency of a network is its ability to remain \emph{effectively} functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the…
A common model of robustness of a graph against random failures has all vertices operational, but the edges independently operational with probability $p$. One can ask for the probability that all vertices can communicate ({\em all-terminal…