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Connections in acyclic hypergraphs

David Maier, Jeffrey D. Ullman
<span title="">1984</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;
of .nodes) that holds in ordinary graph theory can he generalized to hypergraphs.  ...  _ :ependencies are exactly those for which the connections among attributes are defined uniquely. H. 0 P!  ...  Connections in a+ic hypergraphs  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(84)90030-6">doi:10.1016/0304-3975(84)90030-6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/eqatc7ouezhejkloz4rigwmv6a">fatcat:eqatc7ouezhejkloz4rigwmv6a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170924061842/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/0f9/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMzA0Mzk3NTg0OTAwMzA2.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/83/53/83532fb6f8c0eec425b8985019e8fa76f4fb373a.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(84)90030-6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Polynomial Delay and Space Discovery of Connected and Acyclic Sub-hypergraphs in a Hypergraph [chapter]

Kunihiro Wasa, Takeaki Uno, Kouichi Hirata, Hiroki Arimura
<span title="">2013</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;
Then, we present an efficient depth-first algorithm that finds all connected and Berge acyclic sub-hypergraphs S in a hypergraph H with m hyperedges and n vertices in O(nm 2 ) time per solution (delay)  ...  We employ the class of connected and Berge acyclic sub-hypergraphs as definition of tree-like substructures, which is the most restricted notion of acyclicities for hypergraphs.  ...  This research was partly supported by MEXT Grantin-Aid for Scientific Research (A), 24240021, FY2012 2015, and Grant-in-Aid for JSPS Fellows (25·1149).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-40897-7_21">doi:10.1007/978-3-642-40897-7_21</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/oewmcpi5bbabxjoq6sfldw4x54">fatcat:oewmcpi5bbabxjoq6sfldw4x54</a> </span>
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On the desirability of omega-acyclic database schemes

Nguyễn Văn Định
<span title="2012-08-01">2012</span> <i title="Publishing House for Science and Technology, Vietnam Academy of Science and Technology"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/x6rvdhhbgrgmrbjsa2vpyeos5e" style="color: black;">Journal of Computer Science and Cybernetics</a> </i> &nbsp;
We first prove that with this class given here, the notion of acyclic hypergraphs used by graph theorists is equivalent to the notion, in the sense relevant to database theories.  ...  In this paper we study a subclass of acyclic database schemes, the wacyclic database schemes and someclosely related problems.  ...  That mean its hypergraphs consist of a single connected component and it is called connected hypergraph.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.15625/1813-9663/17/3/2626">doi:10.15625/1813-9663/17/3/2626</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ruqrd5fnofazfdbwlsvuu67oc4">fatcat:ruqrd5fnofazfdbwlsvuu67oc4</a> </span>
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On the existence of acyclic views in a database scheme

Giorgio Ausiello, Alessandro d'Atri, Marina Moscarini
<span title="">1985</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;
The importance of acyclic database schemes in relational database theory has been pointed out in various contributions in the literature.  ...  In this paper we consider three kinds of acyclicity, called a-, 7-and Berge-acyclicity by , and we approach the problem of the existence of acyclic views in a database scheme.  ...  A hypergraph is connected if all its nodes are pairwise connected (in this paper we consider only connected hypergraphs).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(85)90012-x">doi:10.1016/0304-3975(85)90012-x</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kevduoyy7red7adew3feucl34i">fatcat:kevduoyy7red7adew3feucl34i</a> </span>
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Some characterizations of γ and β-acyclicity of hypergraphs

David Duris
<span title="">2012</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;
The notions of γ and β-acyclicity are two classic generalizations of the acyclicity of graphs to hypergraphs.  ...  Then we present two characterizations, consisting in applying successively a small set of rules, deciding γ and β-acyclicity respectively.  ...  The set of hyperedges S i v that contain v in T i is connected and E i is in S i v . Moreover, the only hyperedge not in T i that contain v is E and it is connected to E i in T .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2012.05.005">doi:10.1016/j.ipl.2012.05.005</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jei2hkmlrnfx7b6i6g6pylbxpm">fatcat:jei2hkmlrnfx7b6i6g6pylbxpm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170706233311/http://cse.unl.edu/~choueiry/Documents/Duris-alpha-beta-acyclic-2008.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/d2/6e/d26ee5165ebd44c01d3183c0b79db4ee6a1f4a00.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.ipl.2012.05.005"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Degrees of acyclicity for hypergraphs and relational database schemes

Ronald Fagin
<span title="1983-07-01">1983</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r72grtxx6jad5hjzl7fxcunwhi" style="color: black;">Journal of the ACM</a> </i> &nbsp;
Each of the degrees of hypergraph acyclicity that we consider is a generalization of the concept of acyclicity for ordinary undirected graphs; that is, an undirected graph is acyclic in the usual sense  ...  1 515 FIGURE 1 FIGURE 2 problems that are NP-complete in general, but which have polynomial-time algorithms under the assumption of a-acyclicity.  ...  The author is grateful to Shel Finkelstein and Jorma Rissanen for interesting discussions about Theorem 8.1(4) that led the author to consider the concept of-y-acyclicity.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2402.322390">doi:10.1145/2402.322390</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/emmduwyygvdj5ekrlrtj7wtwpu">fatcat:emmduwyygvdj5ekrlrtj7wtwpu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20060312044525/http://www.almaden.ibm.com/cs/people/fagin/jacm83b.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/41/5f/415fc39efcf05915976e2d73336c38fe3e240fed.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2402.322390"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

On the hypercompetition numbers of hypergraphs [article]

Boram Park, Yoshio Sano
<span title="2011-02-09">2011</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In particular, we give the exact value of the hypercompetition number of a connected graph.  ...  Any hypergraph with sufficiently many isolated vertices is the competition hypergraph of an acyclic digraph.  ...  We prove by induction on the number of connected components of H. Suppose that H is a connected hypergraph. Let n and t be the numbers of vertices and hyperedges in H, respectively.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.5622v3">arXiv:1005.5622v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jvv5upxr5rf3jbuzomsv4gkdr4">fatcat:jvv5upxr5rf3jbuzomsv4gkdr4</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1005.5622/1005.5622.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> File Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fc/2c/fc2cecd72d844a8649e4575e369ccac6a67ff5bf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1005.5622v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

The NP-completeness of finding A-trails in Eulerian graphs and of finding spanning trees in hypergraphs

Lars Døvling Andersen, Herbert Fleischner
<span title="">1995</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;
Bent and Udi Manber have shown that it is NP-complete to decide whether a simple, 2-connected, plane Eulerian graph has an A-trail, that is, an Eulerian trail in which successive edges are always neighbours  ...  We then apply this result to show that it is NP-complete to decide whether a linear hypergraph which is regular of degree 3 has a spanning tree.  ...  Acyclic hypergraphs in general (not just spanning trees) have been investigated in connection with databases [6] ; we return to this towards the end of the paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(95)80001-k">doi:10.1016/0166-218x(95)80001-k</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ymtqpxxwvzdolgflhnumveuqx4">fatcat:ymtqpxxwvzdolgflhnumveuqx4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170924200659/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/1b4/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMTY2MjE4eDk1ODAwMDFr.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/4c/d4/4cd4354e0a53e45abf22d5ed923c3561433dd898.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0166-218x(95)80001-k"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Generating the fewest redundancy-free scheme trees from acyclic conceptual-model hypergraphs in polynomial time

Wai Yin Mok, Joseph Fong, David W. Embley
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/epn2gc3fozcsphiz3xnhmwom7u" style="color: black;">Information Systems</a> </i> &nbsp;
We show, however, that the problem has a polynomial-time solution if the conceptual-model hypergraph is acyclic.  ...  Generating the fewest redundancy-free scheme trees from conceptual-model hypergraphs is NP-hard [11] .  ...  Embley was supported in part by the National Science Foundation under grant numbers 0083127 and 0414644.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.is.2013.10.009">doi:10.1016/j.is.2013.10.009</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wqjnqmbarrf6hewu4iz465nrxe">fatcat:wqjnqmbarrf6hewu4iz465nrxe</a> </span>
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Pathway analysis with signaling hypergraphs

Anna Ritz, T. M. Murali
<span title="">2014</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7y7p3qrae5bnlok65yvbqtexc4" style="color: black;">Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics - BCB &#39;14</a> </i> &nbsp;
We relate this problem to computing the shortest acyclic B-hyperpath in a signaling hypergraph -an NP-hard problem -and present a mixed integer linear program to solve it.  ...  More accurate representations such as directed hypergraphs remain underutilized. In this paper, we present an extension of a directed hypergraph that we call a signaling hypergraph.  ...  Acyclic B-Connected Sub-Hypergraphs Given a hypergraph H and two hypernodes s and t in VH, we wish to compute an acyclic sub-hypergraph H that contains s and t such that t ∈ B H (s), i.e. t is B-connected  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2649387.2649450">doi:10.1145/2649387.2649450</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/bcb/RitzM14.html">dblp:conf/bcb/RitzM14</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/scjf6b6li5htdem2hc5qvhbm2q">fatcat:scjf6b6li5htdem2hc5qvhbm2q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809003948/https://bioinformatics.cs.vt.edu/~murali/papers/2014-acm-bcb-pathways-signaling-hypergraphs.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/6b/cf/6bcfb89f594485505f11716ba6b33fafb7aa929e.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/2649387.2649450"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Integrating information by outerjoins and full disjunctions (extended abstract)

Anand Rajaraman, Jeffrey D. Ullman
<span title="">1996</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xtq6wnwaszaebg4qf7aw6mllwi" style="color: black;">Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS &#39;96</a> </i> &nbsp;
We prove that there is a natural outerjoin sequence producing the full disjunction if and only if the set of relation schemes forms a connected, -acyclic hypergraph.  ...  The answer involves a concept of from Fagin 1983] called \ -acyclic hypergraphs."  ...  Lemma 5.2: Every connected -acyclic hypergraph of more than one hyperedge has a -decomposition. Proof: Consider connected -acyclic hypergraph H. Construct its Bachman diagram, which m ust be acyclic.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/237661.237717">doi:10.1145/237661.237717</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/pods/RajaramanU96.html">dblp:conf/pods/RajaramanU96</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rayqlkvf5vggtmx7u3ssn4kf64">fatcat:rayqlkvf5vggtmx7u3ssn4kf64</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922003251/http://dbgroup.unimo.it/_domenico/outerjoin.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/66/10/6610fd7e48113c87a7671f8495092a7f4e6edb59.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/237661.237717"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Finding (s,d)-Hypernetworks in F-Hypergraphs is NP-Hard [article]

Reynaldo Gil-Pons, Max Ward, Loïc Miller
<span title="2022-01-14">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We consider the problem of computing an (s,d)-hypernetwork in an acyclic F-hypergraph.  ...  In a surprising contrast, we find that for acyclic F-hypergraphs the problem is NP-hard, which also implies the problem is hard in BF-hypergraphs.  ...  The FHEP in acyclic F-hypergraphs is NP-complete. Proof. Our construction ( ) is an acyclic F-hypergraph (Lemma 2.4).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2201.04799v2">arXiv:2201.04799v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zbjyz23itreg7j2gp4yszeqf2e">fatcat:zbjyz23itreg7j2gp4yszeqf2e</a> </span>
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Acyclic database schemes (of various degrees): A painless introduction [chapter]

Ronald Fagin
<span title="">1983</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;
In a connected join, the set of relation schemes of the relations that are joined is connected.) Figure 10 . 10 2 is y-acyclic.  ...  A reduced hypergraph is said to be acyclic if every closed, connected set of at least three edges has an articulation set.  ... 
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Equivalence between Hypergraph Convexities

Francesco M. Malvestuto, Mauro Mezzini, Marina Moscarini
<span title="">2011</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/uaexvpib2jd2lfsbu2xbwuv6ai" style="color: black;">ISRN Discrete Mathematics</a> </i> &nbsp;
As a result, we obtain a convexity-theoretic characterization of Berge-acyclic hypergraphs and of γ-acyclic hypergraphs.  ...  Next, in order to generalize this result to a connected hypergraph H, in addition to the hypergraph versions of ap -convexity and m-convexity, we consider canonical convexity (or c-convexity) and simple-path  ...  An open problem is the characterization of graphs and, more in general, of hypergraphs in which g-convexity and m-convexity are equivalent.  ... 
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Page 1205 of Automation and Remote Control Vol. 54, Issue 7 [page]

<span title="">1993</span> <i title="Springer Science &amp; Business Media"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_automation-and-remote-control" style="color: black;">Automation and Remote Control </a> </i> &nbsp;
The hypergraph X, = Xp U x” satisfies (3) and does not contain blocks; consequently, according to Lemma 2, it is connected in G,.  ...  we obtain that the R-graph G, of the hypergraph x is connected.  ... 
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