Related papers: $2$-Fault-Tolerant Strong Connectivity Oracles
We study the 2-Disjoint Shortest Paths (2-DSP) problem: given a directed weighted graph and two terminal pairs $(s_1,t_1)$ and $(s_2,t_2)$, decide whether there exist vertex-disjoint shortest paths between each pair. Building on recent…
We study the problem of finding a spanning forest in an undirected, $n$-vertex multi-graph under two basic query models. One is the Linear query model which are linear measurements on the incidence vector induced by the edges; the other is…
In a directed graph $D$ on vertex set $v_1,\dots ,v_n$, a \emph{forward arc} is an arc $v_iv_j$ where $i<j$. A pair $v_i,v_j$ is \emph{forward connected} if there is a directed path from $v_i$ to $v_j$ consisting of forward arcs. In the…
This paper studies a survivable traffic grooming problem in large-scale optical transport networks under double-link failures (STG2). Each communication demand must be assigned a route for every possible scenario involving zero, one, or two…
A graph $G$ is contractible to a graph $H$ if there is a set $X \subseteq E(G)$, such that $G/X$ is isomorphic to $H$. Here, $G/X$ is the graph obtained from $G$ by contracting all the edges in $X$. For a family of graphs $\cal F$, the…
We present an $O(n^{1.5})$-space distance oracle for directed planar graphs that answers distance queries in $O(\log n)$ time. Our oracle both significantly simplifies and significantly improves the recent oracle of Cohen-Addad, Dahlgaard…
Let $S \subseteq \mathbb{R}^2$ be a set of $n$ \emph{sites} in the plane, so that every site $s \in S$ has an \emph{associated radius} $r_s > 0$. Let $D(S)$ be the \emph{disk intersection graph} defined by $S$, i.e., the graph with vertex…
The vertex connectivity of an $m$-edge $n$-vertex undirected graph is the smallest number of vertices whose removal disconnects the graph, or leaves only a singleton vertex. In this paper, we give a reduction from the vertex connectivity…
In this paper, we consider tree decompositions, branch decompositions, and clique decompositions. We improve the running time of dynamic programming algorithms on these graph decompositions for a large number of problems as a function of…
Resistance distance computation is a fundamental problem in graph analysis, yet existing random walk-based methods are limited to approximate solutions and suffer from poor efficiency on small-treewidth graphs (e.g., road networks). In…
There has been recent progress in showing that the exponential dependence on treewidth in dynamic programming algorithms for solving NP-hard problems are optimal under the Strong Exponential Time Hypothesis (SETH). We extend this work to…
An $n$-vertex $m$-edge graph is \emph{$k$-vertex connected} if it cannot be disconnected by deleting less than $k$ vertices. After more than half a century of intensive research, the result by [Li et al. STOC'21] finally gave a…
We present a framework for designing efficient distributed data structures for multi-dimensional data. Our structures, which we call skip-webs, extend and improve previous randomized distributed data structures, including skipnets and skip…
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 a strongly connected directed graph and $u,v,w\in V(G)$ be three vertices. Then $w$ strongly resolves $u$ to $v$ if there is a shortest $u$-$w$-path containing $v$ or a shortest $w$-$v$-path containing $u$. A set $R\subseteq…
A natural requirement of many distributed structures is fault-tolerance: after some failures, whatever remains from the structure should still be effective for whatever remains from the network. In this paper we examine spanners of general…
We investigate the tractability of a simple fusion of two fundamental structures on graphs, a spanning tree and a perfect matching. Specifically, we consider the following problem: given an edge-weighted graph, find a minimum-weight…
We consider the problem of constructing a communication infrastructure from scratch, for a collection of identical wireless nodes. Combinatorially, this means a) finding a set of links that form a strongly connected spanning graph on a set…
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,…
Inspired by the classical fractional cascading technique, we introduce new techniques to speed up the following type of iterated search in 3D: The input is a graph $\mathbf{G}$ with bounded degree together with a set $H_v$ of 3D hyperplanes…