Related papers: Improved Distance Sensitivity Oracles with Subcubi…

We revisit the problem of privately releasing the all-pairs shortest path distances of a weighted undirected graph up to low additive error, which was first studied by Sealfon [Sea16]. In this paper, we improve significantly on Sealfon's…

Consider the following "local" cut-detection problem in a directed graph: We are given a seed vertex $x$ and need to remove at most $k$ edges so that at most $\nu$ edges can be reached from $x$ (a "local" cut) or output $\bot$ to indicate…

Let $\mathcal{P}$ be a set of $h$ pairwise-disjoint polygonal obstacles with a total of $n$ vertices in the plane. We consider the problem of building a data structure that can quickly compute an $L_1$ shortest obstacle-avoiding path…

Let $G$ be an unweighted, undirected graph. An additive $k$-spanner of $G$ is a subgraph $H$ that approximates all distances between pairs of nodes up to an additive error of $+k$, that is, it satisfies $d_H(u,v) \le d_G(u,v)+k$ for all…

Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with $o(mn)$ total update time, where $m$ is the number of edges and $n$ is the…

In the decremental single-source shortest paths (SSSP) problem we want to maintain the distances between a given source node $s$ and every other node in an $n$-node $m$-edge graph $G$ undergoing edge deletions. While its static counterpart…

In this paper we study the Steiner tree problem over a dynamic set of terminals. We consider the model where we are given an $n$-vertex graph $G=(V,E,w)$ with positive real edge weights, and our goal is to maintain a tree which is a good…

Let $G$ be an $n$-node and $m$-edge positively real-weighted undirected graph. For any given integer $f \ge 1$, we study the problem of designing a sparse \emph{f-edge-fault-tolerant} ($f$-EFT) $\sigma${\em -approximate single-source…

The Hausdorff distance is a metric commonly used to compute the set similarity of geometric sets. For sets containing a total of $n$ points, the exact distance can be computed na\"{i}vely in $O(n^2)$ time. In this paper, we show how to…

We study algorithms for spectral graph sparsification. The input is a graph $G$ with $n$ vertices and $m$ edges, and the output is a sparse graph $\tilde{G}$ that approximates $G$ in an algebraic sense. Concretely, for all vectors $x$ and…

Proximity graph-based methods have emerged as a leading paradigm for approximate nearest neighbor (ANN) search in the system community. This paper presents fresh insights into the theoretical foundation of these methods. We describe an…

In this paper we present an efficient reachability oracle under single-edge or single-vertex failures for planar directed graphs. Specifically, we show that a planar digraph $G$ can be preprocessed in $O(n\log^2{n}/\log\log{n})$ time,…

In this paper, we provide faster algorithms for computing various fundamental quantities associated with random walks on a directed graph, including the stationary distribution, personalized PageRank vectors, hitting times, and escape…

The area of sublinear algorithms have recently received a lot of attention. In this setting, one has to choose specific access model for the input, as the algorithm does not have time to pre-process or even to see the whole input. A…

We give an algorithm to find a minimum cut in an edge-weighted directed graph with $n$ vertices and $m$ edges in $\tilde O(n\cdot \max(m^{2/3}, n))$ time. This improves on the 30 year old bound of $\tilde O(nm)$ obtained by Hao and Orlin…

In the pairwise weighted spanner problem, the input consists of an $n$-vertex-directed graph, where each edge is assigned a cost and a length. Given $k$ vertex pairs and a distance constraint for each pair, the goal is to find a…

Depth first search (DFS) tree is a fundamental data structure for solving graph problems. The classical algorithm [SiComp74] for building a DFS tree requires $O(m+n)$ time for a given graph $G$ having $n$ vertices and $m$ edges. Recently,…

Many graph processing algorithms require determination of shortest-path distances between arbitrary numbers of node pairs. Since computation of exact distances between all node-pairs of a large graph, e.g., 10M nodes and up, is…

The min-distance between two nodes $u, v$ is defined as the minimum of the distance from $v$ to $u$ or from $u$ to $v$, and is a natural distance metric in DAGs. As with the standard distance problems, the Strong Exponential Time Hypothesis…

Given an $n$-vertex $m$-edge digraph $G = (V,E)$ and a set $S \subseteq V$, $|S| = n^{\sigma}$ (for some $0 < \sigma \le 1$) of designated sources, the $S \times V$-direachability problem is to compute for every $s \in S$, the set of all…