Related papers: Improved Online Reachability Preservers
The discrete Fr\'echet distance is a popular measure for comparing polygonal curves. An important variant is the discrete Fr\'echet distance under translation, which enables detection of similar movement patterns in different spatial…
Graph separation is a central tool in parameterized algorithm design, and important separators are among its most successful ingredients. They yield small, structured families of separators that can be enumerated efficiently, and underlie…
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…
Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges (Patnaik and Immerman…
We examine the problem of maximizing the reachability of a given source in temporal graphs that are given as the union of k temporal paths, i.e., every given path is a sequence of edges with strictly increasing labels that denote…
We introduce a technique for reachability analysis of Time-Basic (TB) Petri nets, a powerful formalism for real- time systems where time constraints are expressed as intervals, representing possible transition firing times, whose bounds are…
We study the problem of compressing a weighted graph $G$ on $n$ vertices, building a "sketch" $H$ of $G$, so that given any vector $x \in \mathbb{R}^n$, the value $x^T L_G x$ can be approximated up to a multiplicative $1+\epsilon$ factor…
Probabilistic guarantees of safety and performance are important in constrained dynamical systems with stochastic uncertainty. We consider the stochastic reachability problem, which maximizes the probability that the state remains within…
Persistence diagrams are important tools in the field of topological data analysis that describe the presence and magnitude of features in a filtered topological space. However, current approaches for comparing a persistence diagram to a…
We introduce a new algorithmic framework for designing dynamic graph algorithms in minor-free graphs, by exploiting the structure of such graphs and a tool called vertex sparsification, which is a way to compress large graphs into small…
A $t$-bar visibility representation of a graph assigns each vertex up to $t$ horizontal bars in the plane so that two vertices are adjacent if and only if some bar for one vertex can see some bar for the other via an unobstructed vertical…
This paper discusses the reliability of a graph in which the links are perfectly reliable but the nodes may fail with certain probability p. Calculating graph node reliability is an NP-Hard problem. We introduce an efficient and accurate…
We study the existence and construction of sparse supports for hypergraphs derived from subgraphs of a graph $G$. For a hypergraph $(X,\mathcal{H})$, a support $Q$ is a graph on $X$ s.t. $Q[H]$, the graph induced on vertices in $H$ is…
In the sensitive distance oracle problem, there are three phases. We first preprocess a given directed graph $G$ with $n$ nodes and integer weights from $[-W,W]$. Second, given a single batch of $f$ edge insertions and deletions, we update…
Controlling real-world networked systems, including ecological, biomedical, and engineered networks that exhibit higher-order interactions, remains challenging due to inherent nonlinearities and large system scales. Despite extensive…
Betweenness centrality is a classic measure that quantifies the importance of a graph element (vertex or edge) according to the fraction of shortest paths passing through it. This measure is notoriously expensive to compute, and the best…
The 2-Vertex-Connected Spanning Subgraph problem (2VCSS) is among the most basic NP-hard (Survivable) Network Design problems: we are given an (unweighted) undirected graph $G$. Our goal is to find a spanning subgraph $S$ of $G$ with the…
Computing the Strongly-Connected Components (SCCs) in a graph $G=(V,E)$ is known to take only $O(m + n)$ time using an algorithm by Tarjan from 1972[SICOMP 72] where $m = |E|$, $n=|V|$. For fully-dynamic graphs, conditional lower bounds…
Given a graph $G=(V,E)$, capacities $w(e)$ on edges, and a subset of terminals $\mathcal{T} \subseteq V: |\mathcal{T}| = k$, a mimicking network for $(G,\mathcal{T})$ is a graph $(H,w')$ that contains copies of $\mathcal{T}$ and preserves…
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…