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About 382 papers for “Transitive reduction”
Roderic Page · Front Matter · 2007
Quick note to self, having stumbled on the Wikipedia page on transitive reduction. Given a graph like this: the transitive reduction is: Note that the original graph has an edge a -> d, but this is absent after the reduction because we can get from a to d via b (or c). What's the point?
Cited by 0Open access
Roderic Page · Front Matter · 2007
Quick note to self, having stumbled on the Wikipedia page on transitive reduction. Given a graph like this: the transitive reduction is: Note that the original graph has an edge a -> d, but this is absent after the reduction because we can get from a to d via b (or c). What's the point?
Cited by 0Open access
Ouahiba Bessouf, Abdelkader Khelladi, Thomas Zasĺavsky · Czechoslovak Mathematical Journal · 2019
In a bidirected graph an edge has a direction at each end, so bidirected graphs generalize directed graphs. We generalize the definitions of transitive closure and transitive reduction from directed graphs to bidirected graphs by introducing new notions of bipath and bicircuit that generalize directed paths and cycles. We show how transitive reduction is related to transitive closure and to the matroids of the signed graph corresponding to the bidirected graph.
Cited by 0Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2014
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network. The paper can be found at http://arxiv.org/abs/1310.8224
Cited by 0Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2014
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network. The paper can be found at http://arxiv.org/abs/1310.8224
Cited by 0Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2013
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network. The paper can be found at http://arxiv.org/abs/1310.8224
Cited by 1Open access
James R. Clough, J. Gollings, Tamar Loach · Figshare · 2014
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network. The paper can be found at http://arxiv.org/abs/1310.8224
Cited by 46Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2014
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network. The paper can be found at http://arxiv.org/abs/1310.8224
Cited by 0Open access
Clough, James, Evans, Tim, Loach, Tamar · Figshare · 2014
New version of the arXiv paper 'Transitive reduction of citation networks'
Cited by 0Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2014
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network. The paper can be found at http://arxiv.org/abs/1310.8224
Cited by 0Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2013
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network. The paper can be found at http://arxiv.org/abs/1310.8224
Cited by 0Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2013
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network
Cited by 0Open access
James R. Clough, Tim Evans, Tamar Loach · Figshare · 2013
Analysis of the Transitive Reduction of citations networks as a tool to reveal causal structure and highlight edges more likely to correspond to information transfer in a network
Cited by 0Open access
Gramoz Goranci, Adam Karczmarz, Ali Momeni et al. · ArXiv.org · 2025
Given a directed graph $G$, a transitive reduction $G^t$ of $G$ (first studied by Aho, Garey, Ullman [SICOMP `72]) is a minimal subgraph of $G$ that preserves the reachability relation between every two vertices in $G$. In this paper, we study the computational complexity of transitive reduction in the dynamic setting. We obtain the first fully dynamic algorithms for maintaining a transitive reduction of a general directed graph undergoing updates such as edge insertions or deletions. Our first algorithm achieves $O(m+n \log n)$ amortized update time, which is near-optimal for sparse directed graphs, and can even support extended update operations such as inserting a set of edges all incident to the same vertex, or deleting an arbitrary set of edges. Our second algorithm relies on fast matrix multiplication and achieves $O(m+ n^{1.585})$ \emph{worst-case} update time.
Cited by 0Open access
Phillip B. Gibbons, Richard M. Karp, Vijaya Ramachandran et al. · 1988
COSATI COOES 18 SUBJECT TERMS (Corrtnue o n reverse if necessory ond identify by block num ber)directed graphs, graph algorithms, PRAM algorithms, directed spanning trees.We study the following problem: given a strongly connected digraph, find a minimal strongly connected spanning subgraph of it Our mam result is a paralle algorithm for this problem, which runs in polylog parallel time and uses O (n ) pro cessors on a PRAM.Our algorithm is simple and the major tool it uses is comput ing a minimum-weight branching with zero-one weights.We also present sequen tial algorithms for the problem that run in time 0( m +n logn ).22a.
Cited by 3
Phillip B. Gibbons, Richard M. Karp, Vijaya Remachandran et al. · 1988
Cited by 0
Klaus Simon · Lecture notes in computer science · 1988
Cited by 5
Goranci, Gramoz, Karczmarz, Adam, Momeni, Ali et al. · DROPS (Schloss Dagstuhl – Leibniz Center for Informatics) · 2025
Given a directed graph G, a transitive reduction G^t of G (first studied by Aho, Garey, Ullman [SICOMP `72]) is a minimal subgraph of G that preserves the reachability relation between every two vertices in G. In this paper, we study the computational complexity of transitive reduction in the dynamic setting. We obtain the first fully dynamic algorithms for maintaining a transitive reduction of a general directed graph undergoing updates such as edge insertions or deletions. Our first algorithm achieves O(m+n log n) amortized update time, which is near-optimal for sparse directed graphs, and can even support extended update operations such as inserting a set of edges all incident to the same vertex, or deleting an arbitrary set of edges. Our second algorithm relies on fast matrix multiplication and achieves O(m+ n^{1.585}) worst-case update time.
Cited by 0Open access
Xiaoqin Zhan, Suyun Ding · Discrete Mathematics · 2018
Cited by 4
Hiroshi Hashimoto · Discrete Applied Mathematics · 1984
Cited by 2