相关论文: Vertex Fault-Tolerant Geometric Spanners for Weigh…

The greedy spanner is the highest quality geometric spanner (in e.g. edge count and weight, both in theory and practice) known to be computable in polynomial time. Unfortunately, all known algorithms for computing it take Omega(n^2) time,…

Let $H$ be an edge-weighted graph, and let $G$ be a subgraph of $H$. We say that $G$ is an $f$-fault-tolerant $t$-spanner for $H$, if the following is true for any subset $F$ of at most $f$ edges of $G$: For any two vertices $p$ and $q$,…

In this article, we present a construction of a spanner on a set of $n$ points in $\mathbf{R}^d$ that we call a heavy path WSPD spanner. The construction is parameterized by a constant $s > 2$ called the separation ratio. The size of the…

An \emph{additive $+\beta$ spanner} of a graph $G$ is a subgraph which preserves distances up to an additive $+\beta$ error. Additive spanners are well-studied in unweighted graphs but have only recently received attention in weighted…

Motivated by multipath routing, we introduce a multi-connected variant of spanners. For that purpose we introduce the $p$-multipath cost between two nodes $u$ and $v$ as the minimum weight of a collection of $p$ internally vertex-disjoint…

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…

Given a connected graph $G=(V,E)$ and a length function $\ell:E\to {\mathbb R}$ we let $d_{v,w}$ denote the shortest distance between vertex $v$ and vertex $w$. A $t$-spanner is a subset $E'\subseteq E$ such that if $d'_{v,w}$ denotes…

We show that the greedy spanner algorithm constructs a $(1+\epsilon)$-spanner of weight $\epsilon^{-O(d)}w(\mathrm{MST})$ for a point set in metrics of doubling dimension $d$, resolving an open problem posed by Gottlieb. Our result…

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…

Let $P \subset \mathbb{R}^2$ be a planar $n$-point set such that each point $p \in P$ has an associated radius $r_p > 0$. The transmission graph $G$ for $P$ is the directed graph with vertex set $P$ such that for any $p, q \in P$, there is…

Given complex numbers $w_1, \ldots, w_n$, we define the weight $w(X)$ of a set $X$ of 0-1 vectors as the sum of $w_1^{x_1} \cdots w_n^{x_n}$ over all vectors $(x_1, \ldots, x_n)$ in $X$. We present an algorithm, which for a set $X$ defined…

A geometric $t$-spanner $\mathcal{G}$ on a set $S$ of $n$ point sites in a metric space $P$ is a subgraph of the complete graph on $S$ such that for every pair of sites $p,q$ the distance in $\mathcal{G}$ is a most $t$ times the distance…

Ahmed, Bodwin, Sahneh, Kobourov, and Spence (WG 2020) introduced additive spanners for weighted graphs and constructed (i) a $+2W_{\max}$ spanner with $O(n^{3/2})$ edges and (ii) a $+4W_{\max}$ spanner with $\tilde{O}(n^{7/5})$ edges, and…

Let $P$ be a set of $n$ points in $\mathbb{R}^d$, and let $\varepsilon,\psi \in (0,1)$ be parameters. Here, we consider the task of constructing a $(1+\varepsilon)$-spanner for $P$, where every edge might fail (independently) with…

For a graph $G$ and a non-negative integral weight function $w$ on the vertex set of $G$, a set $S$ of vertices of $G$ is $w$-safe if $w(C)\geq w(D)$ for every component $C$ of the subgraph of $G$ induced by $S$ and every component $D$ of…

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…

In this paper we devise a novel \emph{unified} construction of Euclidean spanners that trades between the maximum degree, diameter and weight gracefully. For a positive integer k, our construction provides a (1+eps)-spanner with maximum…

We initiate the study on fault-tolerant spanners in hypergraphs and develop fast algorithms for their constructions. A fault-tolerant (FT) spanner preserves approximate distances under network failures, often used in applications like…

In this paper we address the problem of computing a sparse subgraph of a weighted directed graph such that the exact distances from a designated source vertex to all other vertices are preserved under bounded weight increment. Finding a…

Random geometric graphs are a popular choice for a latent points generative model for networks. Their definition is based on a sample of $n$ points $X_1,X_2,\cdots,X_n$ on the Euclidean sphere~$\mathbb{S}^{d-1}$ which represents the latent…