相关论文: Relaxed spanners for directed disk graphs
A spanner is a sparse subgraph of a given graph $G$ which preserves distances, measured w.r.t.\ some distance metric, up to a multiplicative stretch factor. This paper addresses the problem of constructing graph spanners w.r.t.\ the group…
In this paper we study the diameter of the random graph $G(n,p)$, i.e., the the largest finite distance between two vertices, for a wide range of functions $p=p(n)$. For $p=\la/n$ with $\la>1$ constant, we give a simple proof of an…
We present an algorithm which computes a planar 2-spanner from an Unit Disk Graph when the node density is sufficient. The communication complexity in terms of number of node's identifier sent by the algorithm is $6n$, while the…
We study the problem of maintaining a lightweight bounded-degree $(1+\varepsilon)$-spanner of a dynamic point set in a $d$-dimensional Euclidean space, where $\varepsilon>0$ and $d$ are arbitrary constants. In our fully-dynamic setting,…
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,…
$\renewcommand{\Re}{\mathbb{R}}$We present a new optimal construction of a semi-separated pair decomposition (i.e., SSPD) for a set of $n$ points in $\Re^d$. In the new construction each point participates in a few pairs, and it extends…
In this paper we initiate the study of expander decompositions of a graph $G=(V, E)$ in the streaming model of computation. The goal is to find a partitioning $\mathcal{C}$ of vertices $V$ such that the subgraphs of $G$ induced by the…
A \emph{$\nu$-reliable spanner} of a metric space $(X,d)$, is a (dominating) graph $H$, such that for any possible failure set $B\subseteq X$, there is a set $B^+$ just slightly larger $|B^+|\le(1+\nu)\cdot|B|$, and all distances between…
Spectral sparsification for directed Eulerian graphs is a key component in the design of fast algorithms for solving directed Laplacian linear systems. Directed Laplacian linear system solvers are crucial algorithmic primitives to fast…
We study distance preservers, hopsets, and shortcut sets in $n$-node, $m$-edge directed graphs, and show improved bounds and new reductions for various settings of these problems. Our first set of results is about exact and approximate…
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…
We address the following problem: Given a complete $k$-partite geometric graph $K$ whose vertex set is a set of $n$ points in $\mathbb{R}^d$, compute a spanner of $K$ that has a ``small'' stretch factor and ``few'' edges. We present two…
Let $G = (V,E)$ be an undirected graph with maximum degree $\Delta$ and vertex conductance $\Psi^*(G)$. We show that there exists a symmetric, stochastic matrix $P$, with off-diagonal entries supported on $E$, whose spectral gap…
Expander graphs have been recently proposed to construct efficient compressed sensing algorithms. In particular, it has been shown that any $n$-dimensional vector that is $k$-sparse (with $k\ll n$) can be fully recovered using…
We give a simple algorithm for maintaining a $n^{o(1)}$-approximate spanner $H$ of a graph $G$ with $n$ vertices as $G$ receives edge updates by reduction to the dynamic All-Pairs Shortest Paths (APSP) problem. Given an initially empty…
A $t$-spanner of a weighted undirected graph $G=(V,E)$, is a subgraph $H$ such that $d_H(u,v)\le t\cdot d_G(u,v)$ for all $u,v\in V$. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all…
We present a simple greedy procedure to compute an $(\alpha,\beta)$-spanner for a graph $G$. We then show that this procedure is useful for building fault-tolerant spanners, as well as spanners for weighted graphs. Our first main result is…
Given a set of $n$ sites from $\mathbb{R}^d$, each having some positive weight factor, the Multiplicatively Weighted Voronoi Diagram is a subdivision of space that associates each cell to the site whose weighted Euclidean distance is…
In a directed graph $G$ with non-correlated edge lengths and costs, the \emph{network design problem with bounded distances} asks for a cost-minimal spanning subgraph subject to a length bound for all node pairs. We give a bi-criteria…
In this paper we consider the problem of efficiently constructing $k$-vertex fault-tolerant geometric $t$-spanners in $\dspace$ (for $k \ge 0$ and $t >1$). Vertex fault-tolerant spanners were introduced by Levcopoulus et. al in 1998. For…