Related papers: Efficient Algorithms for Constructing Very Sparse …
Graph spanners are fundamental graph structures with a wide range of applications in distributed networks. We consider a standard synchronous message passing model where in each round $O(\log n)$ bits can be transmitted over every edge (the…
Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling…
In the distributed setting, the only existing constructions of \textit{sparse skeletons}, (i.e., subgraphs with $O(n)$ edges) either use randomization or large messages, or require $\Omega(D)$ time, where $D$ is the hop-diameter of the…
This paper presents efficient distributed algorithms for a number of fundamental problems in the area of graph sparsification: We provide the first deterministic distributed algorithm that computes an ultra-sparse spanner in…
Spanners have been shown to be a powerful tool in graph algorithms. Many spanner constructions use a certain type of clustering at their core, where each cluster has small diameter and there are relatively few spanner edges between…
Near-additive (aka $(1+\epsilon,\beta)$-) emulators and spanners are a fundamental graph-algorithmic construct, with numerous applications for computing approximate shortest paths and related problems in distributed, streaming and dynamic…
Let $G = (V,E,w)$ be a weighted undirected graph on $|V| = n$ vertices and $|E| = m$ edges, let $k \ge 1$ be any integer, and let $\epsilon < 1$ be any parameter. We present the following results on fast constructions of spanners with…
We address the fundamental network design problem of constructing approximate minimum spanners. Our contributions are for the distributed setting, providing both algorithmic and hardness results. Our main hardness result shows that an…
Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse…
We consider the distributed and parallel construction of low-diameter decompositions with strong diameter for (weighted) graphs and (weighted) graphs that can be separated through $k \in \tilde{O}(1)$ shortest paths. This class of graphs…
We use exponential start time clustering to design faster and more work-efficient parallel graph algorithms involving distances. Previous algorithms usually rely on graph decomposition routines with strict restrictions on the diameters of…
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…
Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse…
Given parameters $\alpha\geq 1,\beta\geq 0$, a subgraph $G'=(V,H)$ of an $n$-vertex unweighted undirected graph $G=(V,E)$ is called an $(\alpha,\beta)$-spanner if for every pair $u,v\in V$ of vertices, $d_{G'}(u,v)\leq \alpha…
Over the past decade, there has been increasing interest in distributed/parallel algorithms for processing large-scale graphs. By now, we have quite fast algorithms -- usually sublogarithmic-time and often $poly(\log\log n)$-time, or even…
A $t$-{\em spanner} $H$ of a weighted graph $G=(V,E,w)$ is a subgraph that approximates all pairwise distances up to a factor of $t$. The {\em lightness} of $H$ is defined as the ratio between the weight of $H$ to that of the minimum…
To our knowledge, there are only two known algorithms for constructing sparse and light spanners for general graphs. One of them is the greedy algorithm of Alth$\ddot{o}$fer et al. \cite{ADDJS93}, analyzed by Chandra et al. in SoCG'92. The…
A spanner of a graph is a subgraph that preserves lengths of shortest paths up to a multiplicative distortion. For every $k$, a spanner with size $O(n^{1+1/k})$ and stretch $(2k+1)$ can be constructed by a simple centralized greedy…
Finding sparse cuts is an important tool in analyzing large-scale distributed networks such as the Internet and Peer-to-Peer networks, as well as large-scale graphs such as the web graph, online social communities, and VLSI circuits. In…
We (nearly) settle the time complexity for computing vertex fault-tolerant (VFT) spanners with optimal sparsity (up to polylogarithmic factors). VFT spanners are sparse subgraphs that preserve distance information, up to a small…