Related papers: Reachability and Distances under Multiple Changes
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
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…
Dyck reachability is the standard formulation of a large domain of static analyses, as it achieves the sweet spot between precision and efficiency, and has thus been studied extensively. Interleaved Dyck reachability (denoted $D_k\odot…
We establish and generalise several bounds for various random walk quantities including the mixing time and the maximum hitting time. Unlike previous analyses, our derivations are based on rather intuitive notions of local expansion…
We study reachability and shortest paths problems in dynamic directed graphs. Whereas algebraic dynamic data structures supporting edge updates and reachability/distance queries have been known for quite a long time, they do not, in…
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…
Reachability and other path-based measures on temporal graphs can be used to understand spread of infection, information, and people in modelled systems. Due to delays and errors in reporting, temporal graphs derived from data are unlikely…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…
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…
We consider labeling nodes of a directed graph for reachability queries. A reachability labeling scheme for such a graph assigns a binary string, called a label, to each node. Then, given the labels of nodes $u$ and $v$ and no other…
We study how we can accelerate the spreading of information in temporal graphs via shifting operations; a problem that captures real-world applications varying from information flows to distribution schedules. In a temporal graph there is a…
We present practical linear and almost linear-time algorithms to compute a chain decomposition of a directed acyclic graph (DAG), $G=(V,E)$. The number of vertex-disjoint chains computed is very close to the minimum. The time complexity of…
Let $P$ be a set of $n$ points in the plane where each point $p$ of $P$ is associated with a radius $r_p>0$.The transmission graph $G=(P,E)$ of $P$ is defined as the directed graph such that $E$ contains an edge from $p$ to $q$ if and only…
Finding patterns in graphs is a fundamental problem in databases and data mining. In many applications, graphs are temporal and evolve over time, so we are interested in finding durable patterns, such as triangles and paths, which persist…
A temporal graph is a dynamic graph where every edge is assigned a set of integer time labels that indicate at which discrete time step the edge is available. In this paper, we study how changes of the time labels, corresponding to delays…
In this paper, we consider reachability oracles and reachability preservers for directed graphs/networks prone to edge/node failures. Let $G = (V, E)$ be a directed graph on $n$-nodes, and $P\subseteq V\times V$ be a set of vertex pairs in…
In this work we introduce the graph-theoretic notion of mendability: for each locally checkable graph problem we can define its mending radius, which captures the idea of how far one needs to modify a partial solution in order to "patch a…
Finding the shortest path distance between an arbitrary pair of vertices is a fundamental problem in graph theory. A tremendous amount of research has been successfully attempted on this problem, most of which is limited to static graphs.…
Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing.…
Given a graph $G$ and two independent sets of same size, the Independent Set Reconfiguration Problem under token sliding ask whether one can, in a step by step manner, transform the first independent set into the second one. In each step we…