Related papers: Subsetwise and Multi-Level Additive Spanners with …

The approximate single-source shortest-path problem is as follows: given a graph with nonnegative edge weights and a designated source vertex $s$, return estimates of the distances from~$s$ to each other vertex such that the estimate falls…

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…

In this paper, we study weakly dynamic undirected graphs, that can be used to represent some logistic networks. The goal is to deliver all the delivery points in the network. The network exists in a mostly stable environment, except for a…

Spanners for low dimensional spaces (e.g. Euclidean space of constant dimension, or doubling metrics) are well understood. This lies in contrast to the situation in high dimensional spaces, where except for the work of Har-Peled, Indyk and…

We present an algebraic approach to the watershed adapted to edge or node weighted graphs. Starting with the flooding adjunction, we introduce the flooding graphs, for which node and edge weights may be deduced one from the other. Each node…

Computing \emph{all best swap edges} (ABSE) of a spanning tree $T$ of a given $n$-vertex and $m$-edge undirected and weighted graph $G$ means to select, for each edge $e$ of $T$, a corresponding non-tree edge $f$, in such a way that the…

We study the spectral implications of re-weighting a graph by the $\ell_\infty$-Lewis weights of its edges. Our main motivation is the ER-Minimization problem (Saberi et al., SIAM'08): Given an undirected graph $G$, the goal is to find…

Given a graph $G$ and a digraph $D$ whose vertices are the edges of $G$, we investigate the problem of finding a spanning tree of $G$ that satisfies the constraints imposed by $D$. The restrictions to add an edge in the tree depend on its…

For a given graph $G$, a "hopset" $H$ with hopbound $\beta$ and stretch $\alpha$ is a set of edges such that between every pair of vertices $u$ and $v$, there is a path with at most $\beta$ hops in $G \cup H$ that approximates the distance…

A sparsifier of a graph $G$ (Bencz\'ur and Karger; Spielman and Teng) is a sparse weighted subgraph $\tilde G$ that approximately retains the cut structure of $G$. For general graphs, non-trivial sparsification is possible only by using…

In this paper, we study the problem of finding a minimum weight spanning tree that contains each vertex in a given subset $V_{\rm NT}$ of vertices as an internal vertex. This problem, called Minimum Weight Non-Terminal Spanning Tree,…

This paper introduces an extended notion of expansion suitable for radio networks. A graph $G=(V,E)$ is called an $(\alpha_w, \beta_w)$-{wireless expander} if for every subset $S \subseteq V$ s.t. $|S|\leq \alpha_w \cdot |V|$, there exists…

We consider the problem of computing an approximate weighted shortest path in a weighted subdivision, with weights assigned from the set $\{0, 1, \infty\}$. We present a data structure $B$, which stores a set of convex, non-overlapping…

We find a set of necessary and sufficient conditions under which the weight $w:E\to\mathbb R^+$ on the graph $G=(V,E)$ can be extended to a pseudometric $d:V\times V\to\mathbb R^+$. If these conditions hold and $G$ is a connected graph,…

This paper studies the complexity of distributed construction of purely additive spanners in the CONGEST model. We describe algorithms for building such spanners in several cases. Because of the need to simultaneously make decisions at far…

Let $G = (V, E)$ be an edge-weighted geometric graph such that every edge is horizontal or vertical. The weight of an edge $uv \in E$ is its length. Let $ W_G (u,v)$ denote the length of a shortest path between a pair of vertices $u$ and…

Algorithms for dynamically maintaining minimum spanning trees (MSTs) have received much attention in both the parallel and sequential settings. While previous work has given optimal algorithms for dense graphs, all existing parallel…

We prove that every graph has a spectral sparsifier with a number of edges linear in its number of vertices. As linear-sized spectral sparsifiers of complete graphs are expanders, our sparsifiers of arbitrary graphs can be viewed as…

Increasing the connectivity of a graph is a pivotal challenge in robust network design. The weighted connectivity augmentation problem is a common version of the problem that takes link costs into consideration. The problem is then to find…

We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph $G$, a distance bound $L$, and $p$ pairs of vertices $(s_1,t_1),\cdots,(s_p,t_p)$, the objective is to find a minimum-cost subgraph $G'$…