Related papers: Efficient Labeling for Reachability in Digraphs
We present parallel algorithms for computing single-source reachability and shortest paths on directed $n$-vertex $m$-edge graphs using near-linear $\tilde{O}(m)$ work and $o(\sqrt{n})$ depth whenever $m\ge n^{1+o(1)}$. At the extreme of…
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 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 $n$ .…
The exact path length problem is to determine if there is a path of a given fixed cost between two vertices. This paper focuses on the exact path problem for costs $-1,0$ or $+1$ between all pairs of vertices in an edge-weighted digraph.…
A* is a classic and popular method for graphs search and path finding. It assumes the existence of a heuristic function $h(u,t)$ that estimates the shortest distance from any input node $u$ to the destination $t$. Traditionally, heuristics…
We consider the multi-broadcast problem in arbitrary connected radio networks consisting of $n$ nodes. There are $k$ designated source nodes for some fixed $k \in \{1,\ldots,n\}$, and each source node has a distinct piece of information…
There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move…
A temporal graph is a graph in which vertices communicate with each other at specific time, e.g., $A$ calls $B$ at 11 a.m. and talks for 7 minutes, which is modeled by an edge from $A$ to $B$ with starting time "11 a.m." and duration "7…
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…
In this work we consider temporal graphs, i.e. graphs, each edge of which is assigned a set of discrete time-labels drawn from a set of integers. The labels of an edge indicate the discrete moments in time at which the edge is available. We…
Let $P$ be a set of $n$ points in the plane, where each point $p\in P$ has a transmission radius $r(p)>0$. The transmission graph defined by $P$ and the given radii, denoted by $\mathcal{G}_{\mathrm{tr}}(P)$, is the directed graph whose…
For a given labelled transition system (LTS), synthesis is the task to find an unlabelled Petri net with an isomorphic reachability graph. Even when just demanding an embedding into a reachability graph instead of an isomorphism, a solution…
One of the simplest problems on directed graphs is that of identifying the set of vertices reachable from a designated source vertex. This problem can be solved easily sequentially by performing a graph search, but efficient parallel…
Graph Neural Networks (GNNs) are prominent in handling sparse and unstructured data efficiently and effectively. Specifically, GNNs were shown to be highly effective for node classification tasks, where labelled information is available for…
For a given collection G of directed graphs we define the join-reachability graph of G, denoted by J(G), as the directed graph that, for any pair of vertices a and b, contains a path from a to b if and only if such a path exists in all…
Given an undirected graph $G$, the problem of deciding whether $G$ admits a simple and proper time-labeling that makes it temporally connected is known to be NP-hard (G\"obel et al., 1991). In this article, we relax this problem and ask…
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,…
A fault-tolerant distance labeling scheme assigns a label to each vertex and edge of an undirected weighted graph $G$ with $n$ vertices so that, for any edge set $F$ of size $|F| \leq f$, one can approximate the distance between $p$ and $q$…
In this paper we solve the ancestry-labeling scheme problem which aims at assigning the shortest possible labels (bit strings) to nodes of rooted trees, so that ancestry queries between any two nodes can be answered by inspecting their…
Given a partition of an n element set into equivalence classes, we consider time-space tradeoffs for representing it to support the query that asks whether two given elements are in the same equivalence class. This has various applications…