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An algorithm for transitive reduction of an acyclic graph

David Gries, Alain J. Martin, Jan L.A. van de Snepscheut, Jan Tijmen Udding
<span title="">1989</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hq6x4whtd5hhlhsxzculyeamey" style="color: black;">Science of Computer Programming</a> </i> &nbsp;
Finally, we obtain an algorithm for the transitive reduction of an acyclic graph. We use the following notation.  ...  Introduction We derive a new algorithm for computing the transitive reduction of a directed acyclic graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0167-6423(89)90039-7">doi:10.1016/0167-6423(89)90039-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/dqklkb3dsrb2fbdyx3ckpyfm2i">fatcat:dqklkb3dsrb2fbdyx3ckpyfm2i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190414201251/https://core.ac.uk/download/pdf/82581063.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/cd/79/cd79bf8a60b4a38a201998c6347ba1fcd7be99a5.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0167-6423(89)90039-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

The Transitive Reduction of a Directed Graph

A. V. Aho, M. R. Garey, J. D. Ullman
<span title="">1972</span> <i title="Society for Industrial &amp; Applied Mathematics (SIAM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7dys7zoberdktmxyjciuy5bnse" style="color: black;">SIAM journal on computing (Print)</a> </i> &nbsp;
It is shown that the time complexity of the best algorithm for finding the transitive reduction of a graph is the same as the time to compute the transitive closure of a graph or to perform Boolean matrix  ...  Though directed graphs with cycles may have more than one such representation, we select a natural canonical representative as the transitive reduction for such graphs.  ...  In this paper, we mathematically characterize the transitive reduction and provide an efficient algorithm for computing the transitive reduction of any given directed graph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1137/0201008">doi:10.1137/0201008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ymhisok6wjcn5isrolcbiutm7u">fatcat:ymhisok6wjcn5isrolcbiutm7u</a> </span>
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Lengths of Words Accepted by Nondeterministic Finite Automata [article]

Aaron Potechin, Jeffrey Shallit
<span title="2018-02-13">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that the classic problem of triangle-free graph recognition reduces to this problem, and give an O(n^ω (log n)^1+ϵ log l)-time algorithm to solve it, where ω is the optimal exponent for matrix  ...  First, given such an automaton M of n states, and a length l, does M accept a word of length l?  ...  There is a linear-time reduction from TRIANGLE-FREE GRAPH to NFA LENGTH ACCEPTANCE. The fastest general algorithm for TRIANGLE-FREE GRAPH known runs in O(n ω (log n) 1+ ) time [6, 2, 3] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.04708v1">arXiv:1802.04708v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lkighqzr2fd7vlg6nxt4ajn3km">fatcat:lkighqzr2fd7vlg6nxt4ajn3km</a> </span>
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Page 423 of Mathematical Reviews Vol. , Issue 91A [page]

<span title="">1991</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
(NL-GRON); Udding, Jan Tijmen (NL-GRON) An algorithm for transitive reduction of an acyclic graph. Sci. Comput. Programming 12 (1989), no. 2, 151-155.  ...  However, for an arbitrary digraph, the transitive-reduction problem is NP-complete. The authors propose a new O(n°) algorithm for computing the transitive reduction of an acyclic digraph.  ... 
<span class="external-identifiers"> </span>
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Transitive reduction of a nilpotent boolean matrix

Hiroshi Hashimoto
<span title="">1984</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
The purpose is to present those properties of boolean matrices which are related to finding the transitive reduction of a nilpotent matrix, or an acyclic graph.  ...  Boolean matrices are widely used in many fields, and the theory of boolean matrices is related to the algebra of relations, switching theory, and graph theory.  ...  Acknowledgment The author is grateful to the referees for their constructive remarks in revising this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(84)90078-7">doi:10.1016/0166-218x(84)90078-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/snyw2djqxvfq5gu5aymh2n35ni">fatcat:snyw2djqxvfq5gu5aymh2n35ni</a> </span>
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TRANSWESD: inferring cellular networks with transitive reduction

Steffen Klamt, Robert J. Flassig, Kai Sundmacher
<span title="2010-07-06">2010</span> <i title="Oxford University Press (OUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/4r72gbmtcrde5no3fwwogjs3cu" style="color: black;">Computer applications in the biosciences : CABIOS</a> </i> &nbsp;
Results: We present TRANSWESD, an elaborated variant of TRANSitive reduction for WEighted Signed Digraphs that overcomes conceptual problems of existing versions.  ...  strengths) for recognizing true redundant structures; (iii) causal interpretation of cycles; (iv) relaxed definition of transitive reduction; and (v) approximation algorithms for large networks.  ...  ACKNOWLEDGEMENTS We thank Regina Samaga and Axel von Kamp for commenting on the manuscript and the DREAM4 organizers for creating the in silico challenge and providing data and gold standards.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/bioinformatics/btq342">doi:10.1093/bioinformatics/btq342</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/20605927">pmid:20605927</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC2922889/">pmcid:PMC2922889</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/yvp5hcgbbfdovkzrthipuufsgq">fatcat:yvp5hcgbbfdovkzrthipuufsgq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170815085232/http://pubman.mpdl.mpg.de/pubman/item/escidoc:1755973/component/escidoc:1755972/493348_bioinform_2010.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7c/58/7c58214c893a7889b3fc9a7f738a910d6cb9cc0f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1093/bioinformatics/btq342"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> oup.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2922889" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Page 5452 of Mathematical Reviews Vol. , Issue 88j [page]

<span title="">1988</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A typical reduction is: if there is an algorithm for finding the tran- sitive closure of a Jordan-Dedekind graph in a time linear in the number of edges in the transitive closure, then there is an algo  ...  - rithm for finding the transitive reduction of a Jordan-Dedekind graph in a time linear in the number of edges in the transitive clo- sure.  ... 
<span class="external-identifiers"> </span>
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A Coarse-Grained Parallel Algorithm for Maximal Cliques in Circle Graphs [chapter]

E. N. Cáceres, S. W. Song, J. L. Szwarcfiter
<span title="">2001</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present a parallel algorithm for generating the maximal cliques of a circle graph with n vertices and m edges.  ...  The main contribution is the use of a new technique based on the unrestricted depth search for the design of CGM algorithms.  ...  Graph G R obtained at the end of Step 1 of the parallel algorithm is the transitive reduction of G.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45718-6_69">doi:10.1007/3-540-45718-6_69</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fleaed2sqvhgtbp5jdxwbopyqe">fatcat:fleaed2sqvhgtbp5jdxwbopyqe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190503090636/https://link.springer.com/content/pdf/10.1007%2F3-540-45718-6_69.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f5/4c/f54c1bd5359bbb00d7f24c64f04793de4eea97bb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-45718-6_69"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the Complexity of Singly Connected Vertex Deletion [chapter]

Avinandan Das, Lawqueen Kanesh, Jayakrishnan Madathil, Komal Muluk, Nidhi Purohit, Saket Saurabh
<span title="">2020</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
This problem may be seen as a directed counterpart of the (Undirected) Feedback Vertex Set problem, as an undirected graph is singly connected if and only if it is acyclic.  ...  A digraph D is singly connected if for all ordered pairs of vertices u, v ∈ V (D), there is at most one path in D from u to v.  ...  It would be interesting to see if one can extend the polynomial time algorithm for SCVD on acyclic local tournaments to locally transitive tournaments.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-48966-3_18">doi:10.1007/978-3-030-48966-3_18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vggbtrliyfbsjeljga4p6vtkai">fatcat:vggbtrliyfbsjeljga4p6vtkai</a> </span>
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Efficient reconstruction of biological networks via transitive reduction on general purpose graphics processors

Dragan Bo¿na¿ki, Maximilian R Odenbrett, Anton Wijs, Willem Ligtenberg, Peter Hilbers
<span title="">2012</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/n5zrklrhlzhtdorf4rk4rmeo3i" style="color: black;">BMC Bioinformatics</a> </i> &nbsp;
Results: We develop efficient scalable parallel algorithms for transitive reduction on general purpose graphics processing units for both standard (unweighted) and weighted graphs.  ...  Transitive reduction removes such relations if they can be explained by an indirect path of influences.  ...  Algorithm for unweighted acyclic graphs For obtaining the TR of an unweighted acyclic graph G, typically its transitive closure G T would be calculated first.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1186/1471-2105-13-281">doi:10.1186/1471-2105-13-281</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/23110660">pmid:23110660</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3583792/">pmcid:PMC3583792</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ved25jeoazamlavqyheaugyv7u">fatcat:ved25jeoazamlavqyheaugyv7u</a> </span>
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Lower bounds for testing digraph connectivity with one-pass streaming algorithms [article]

Glencora Borradaile and Claire Mathieu and Theresa Migler
<span title="2014-04-08">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this note, we show that three graph properties - strong connectivity, acyclicity, and reachability from a vertex s to all vertices - each require a working memory of Ω (ϵ m) on a graph with m edges  ...  For upper bounds in directed graphs, there is an algorithm that computes the exact size of the transitive closure using O(m log n) bits of working memory [6] .  ...  Observe that E 1 ∪ E 2 is acyclic iff x i = 0, thus the reduction is complete. Strong connectivity The construction for E 1 is the same as in the acyclic case.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1404.1323v2">arXiv:1404.1323v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5bwgj4jnx5cbdbt63wz6vq2jam">fatcat:5bwgj4jnx5cbdbt63wz6vq2jam</a> </span>
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Parallel Algorithms for Maximal Cliques in Circle Graphs and Unrestricted Depth Search

E. N. Cáceres, S. W. Song, J. L. Szwarcfiter
<span title="2010-06-23">2010</span> <i title="EDP Sciences"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/foywj2stzfcwdln5izx2cxkroe" style="color: black;">RAIRO - Theoretical Informatics and Applications</a> </i> &nbsp;
The maximal cliques generation algorithm is based on generating all maximal paths in a directed acyclic graph, and we present an algorithm for this problem that uses O(log p) communication rounds with  ...  We present parallel algorithms on the BSP/CGM model, with p processors, to count and generate all the maximal cliques of a circle graph with n vertices and m edges.  ...  Output: The transitive reduction G R . 1: for all v i ∈ V in parallel do2: 12: end for Lemma 6.1. Graph G R obtained by Algorithm 5 is the transitive reduction of G. Proof.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1051/ita/2010016">doi:10.1051/ita/2010016</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mtgocalutbctzhbj3z6wxovlsa">fatcat:mtgocalutbctzhbj3z6wxovlsa</a> </span>
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Computing unique canonical covers for simple FDs via transitive reduction

Jens Lechtenbörger
<span title="">2004</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5xfy4fcdxvcvdiybp6iqbffqc4" style="color: black;">Information Processing Letters</a> </i> &nbsp;
First, given an acyclic set F of simple FDs there exists exactly one canonical cover for F . Second, this uniquely determined canonical cover can be computed via transitive reduction.  ...  Third, it is shown how a uniquely determined canonical cover can be fixed in case of arbitrary simple FDs via transitive reduction.  ...  Acknowledgments I would like to thank Gottfried Vossen for convincing me that the results presented in this paper may be of general interest, for drawing my attention to [3] , and for helpful comments  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2004.07.005">doi:10.1016/j.ipl.2004.07.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/xzhxuficvvdk5kfu7htwp5ogcu">fatcat:xzhxuficvvdk5kfu7htwp5ogcu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060926033759/http://dbms.uni-muenster.de/publications/downloads/tech4-04.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4f/a3/4fa3bf97a85381280a62ed892e8618381f8cee9a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2004.07.005"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Fast left-linear semi-unification [chapter]

Fritz Henglein
<span title="">1990</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present a generic polynomial-time algorithm L1 for LLSU, which shows that LLSU is in P.  ...  It is the problem of solving a set of term inequalities M 1 ≤ N 1 , . . . , M k ≤ N k , where ≤ is interpreted as the subsumption preordering on (first-order) terms.  ...  We prove that LLSU is P-complete under log-space reductions, thus giving evidence that there are no fast (NC-class) parallel algorithms for LLSU.  ... 
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<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170808203749/http://www.diku.dk/hjemmesider/ansatte/henglein/papers/henglein1990.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/43/84/4384332d2a0d0f12de42afb44f06a3b9c45e1d5d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-53504-7_64"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

An improved algorithm for transitive closure on acyclic digraphs

Klaus Simon
<span title="">1988</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
In [6] Goralcikova and Koubek describe an algorithm for finding the transitive closure of an acyclic digraph G with worst-case runtime O(n. e",), where n is the number of nodes and ered is the number of  ...  edges in the transitive reduction of G.  ...  Conclusion We presented an improved algorithm for computing the transitive closure of an acyclic digraph with running time O(k* ered), where ered is the number of edges in the transitive reduction and  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(88)90032-1">doi:10.1016/0304-3975(88)90032-1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/upounklozfhujn6swnb4nepihm">fatcat:upounklozfhujn6swnb4nepihm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190415224016/https://core.ac.uk/download/pdf/82238824.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e7/8d/e78d6afdaf427fab85ceb4a65df45bc47c64b5f2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(88)90032-1"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>
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