相关论文: Folklore Sampling is Optimal for Exact Hopsets: Co…

We give the first Congested Clique algorithm that computes a sparse hopset with polylogarithmic hopbound in polylogarithmic time. Given a graph $G=(V,E)$, a $(\beta,\epsilon)$-hopset $H$ with "hopbound" $\beta$, is a set of edges added to…

We prove better lower bounds on additive spanners and emulators, which are lossy compression schemes for undirected graphs, as well as lower bounds on shortcut sets, which reduce the diameter of directed graphs. We show that any $O(n)$-size…

The expansion of a hypergraph, a natural extension of the notion of expansion in graphs, is defined as the minimum over all cuts in the hypergraph of the ratio of the number of the hyperedges cut to the size of the smaller side of the cut.…

Low congestion shortcuts, introduced by Ghaffari and Haeupler (SODA 2016), provide a unified framework for global optimization problems in the congest model of distributed computing. Roughly speaking, for a given graph $G$ and a collection…

The hereditary discrepancy of a set system is a certain quantitative measure of the pseudorandom properties of the system. Roughly, hereditary discrepancy measures how well one can $2$-color the elements of the system so that each set…

For an input graph $G$, an additive spanner is a sparse subgraph $H$ whose shortest paths match those of $G$ up to small additive error. We prove two new lower bounds in the area of additive spanners: 1) We construct $n$-node graphs $G$ for…

A $(\beta,\epsilon)$-$\textit{hopset}$ is, informally, a weighted edge set that, when added to a graph, allows one to get from point $a$ to point $b$ using a path with at most $\beta$ edges ("hops") and length…

We present near-optimal algorithms for detecting small vertex cuts in the CONGEST model of distributed computing. Despite extensive research in this area, our understanding of the vertex connectivity of a graph is still incomplete,…

In this paper, we consider the question of computing sparse subgraphs for any input directed graph $G=(V,E)$ on $n$ vertices and $m$ edges, that preserves reachability and/or strong connectivity structures. We show $O(n+\min\{|{\cal…

We give an $\widetilde{O}(\sqrt{n})$-space single-pass $0.483$-approximation streaming algorithm for estimating the maximum directed cut size (Max-DICUT) in a directed graph on $n$ vertices. This improves over an $O(\log n)$-space $4/9 <…

In this paper we provide a parallel algorithm that given any $n$-node $m$-edge directed graph and source vertex $s$ computes all vertices reachable from $s$ with $\tilde{O}(m)$ work and $n^{1/2 + o(1)}$ depth with high probability in $n$ .…

We propose an efficient $\epsilon$-differentially private algorithm, that given a simple {\em weighted} $n$-vertex, $m$-edge graph $G$ with a \emph{maximum unweighted} degree $\Delta(G) \leq n-1$, outputs a synthetic graph which…

We abstract and study \emph{reachability preservers}, a graph-theoretic primitive that has been implicit in prior work on network design. Given a directed graph $G = (V, E)$ and a set of \emph{demand pairs} $P \subseteq V \times V$, a…

The distributed single-source shortest paths problem is one of the most fundamental and central problems in the message-passing distributed computing. Classical Bellman-Ford algorithm solves it in $O(n)$ time, where $n$ is the number of…

We consider the problem of finding a minimum cut of a weighted graph presented as a single-pass stream. While graph sparsification in streams has been intensively studied, the specific application of finding minimum cuts in streams is less…

Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm…

We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…

The $\mathsf{HYBRID}$ model, introduced in [Augustine et al., SODA '20], provides a theoretical foundation for networks that allow multiple communication modes. The model follows the principles of synchronous message passing, whereas nodes…

We study the problem of computing approximate minimum edge cuts by distributed algorithms. We use a standard synchronous message passing model where in each round, $O(\log n)$ bits can be transmitted over each edge (a.k.a. the CONGEST…

We prove that any $n$-node graph $G$ with diameter $D$ admits shortcuts with congestion $O(\delta D \log n)$ and dilation $O(\delta D)$, where $\delta$ is the maximum edge-density of any minor of $G$. Our proof is simple, elementary, and…