directed graph reachability
What is the reachability relation of a DAG?
The reachability relation of a DAG can be formalized as a partial order ≤ on the vertices of the DAG. In this partial order, two vertices u and v are ordered as u ≤ v exactly when there exists a directed path from u to v in the DAG; that is, when u can reach v (or v is reachable from u ).
What is the reachability relation of a directed graph?
For a directed graph , with vertex set and edge set , the reachability relation of is the transitive closure of , which is to say the set of all ordered pairs of vertices in for which there exists a sequence of vertices such that the edge is in for all .
Is reachability symmetric?
Any pair of vertices in such a graph can reach each other if and only if they belong to the same connected component; therefore, in such a graph, reachability is symmetric ( reaches iff reaches ). The connected components of an undirected graph can be identified in linear time.
Directed Graph
Directed Graphs
Transitive closure of a Graph (Reachability Matrix) #Graph Theory 8
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Improved Dynamic Reachability Algorithms for Directed Graphs
a directed graph and several other algorithms for answering reachability queries without explicitly maintaining a transitive closure matrix. |
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Graph Reachability
Given a directed graph G and two nodes u and v is there a path connecting u to v (denoted u?v)?. 1. 2. 3. 4. 6. 7. 8. 5. 9. |
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1 Path-Tree: An Efficient Reachability Indexing Scheme for Large
Among them graph reachability queries have attracted a lot of research attention. Given two vertices u and v in a directed graph |
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Lecture 7 1 Configuration Graphs and the Reachability Method
Coming back to problems on graphs consider the problem of directed connectivity (denoted conn). Here we are given a directed graph on n-vertices (say |
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Sublinear-Time Decremental Algorithms for Single-Source
31 mai 2016 Reachability and Shortest Paths on Directed Graphs. ?. Monika Henzinger† ... 3.2 Decremental s-t Reachability in Dense Graphs . |
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Efficiently Answering Reachability Queries on Very Large Directed
12 juin 2008 Given two vertices u and v in a directed graph a reachability query asks if there is a path from u to v. Graph reachability is one of the most ... |
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Efficient Labeling for Reachability in Directed Acyclic Graphs
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 |
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A Fully Dynamic Reachability Algorithm for Directed Graphs with an
The dynamic reachability problem i.e. |
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A Fully Dynamic Reachability Algorithm for Directed Graphs with an
The dynamic reachability problem i.e. |
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Join-Reachability Problems in Directed Graphs
Is vertex reachable from vertex ? Reachability Query : Goal: Construct a Data Structure that answers reachability queries efficiently. (Directed) Graph |
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Graph Reachability - HKUST CSE Dept
Graph Reachability Panagiotis Parchas Given a directed graph G and two nodes u and v, is there a path Directed Graph → DAG (directed acyclic graph) by |
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Reachability is harder for directed than for undirected finite graphs
the reachability problem is harder for directed graphs than for undirected graphs simply “graph”, we mean either directed or undirected graph; when it is |
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All-Pairs 2-Reachability in O( log n) Time - CORE
In the 2-reachability problem we are given a directed graph G and we wish to determine if there are two (edge or vertex) disjoint paths from u to v, for given pair |
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Chapter 6 GRAPH REACHABILITY QUERIES: A SURVEY
Graph reachability (or simply reachability) queries, to test whether there is a path from a node to another node in a large directed graph, have being studied [1 |
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A Fully Dynamic Reachability Algorithm for Directed Graphs with an
The dynamic reachability problem, i e , the problem of maintaining a directed graph that undergoes a sequence of edge insertions and deletions in a way that |
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DFS & Directed Graphs
Strong connectivity Connected components in directed graphs defined based on mutual reachability Two vertices in a directed graph are mutually reachable if |
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An Efficient Reachability Indexing Scheme for Large Directed Graphs
Among them, graph reachability queries have attracted a lot of research attention Given two vertices u and v in a directed graph, a reachability query asks if there |
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