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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;
Acyclic join dependenciesThis section is intended for those interested in database dependency theory.  ...  Theorem 7.2 [FMU] A join dependency is acyclic if and only if it is equivalent to a set of multivalued dependencies.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-12727-5_3">doi:10.1007/3-540-12727-5_3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ullpgmbb2nem5cdzkao52mywwy">fatcat:ullpgmbb2nem5cdzkao52mywwy</a> </span>
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Page 2130 of Mathematical Reviews Vol. , Issue 85e [page]

<span title="">1985</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;
Hull, Richard (1-SCA-C) 85¢:68015 Acyclic join dependency and data base projections. J. Comput.  ...  This condition is shown to be necessary in case the original join dependency is acyclic.  ... 
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On acyclic database decompositions

Catriel Beeri, Moshe Y. Vardi
<span title="">1984</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/fbkexx2qg5anljkxraobuswdq4" style="color: black;">Information and Control</a> </i> &nbsp;
It is proved here that when the decomposition, viewed as a hypergraph, is acyclic and the given dependencies are full implicational dependencies, then the reconstruction map is the natural join.  ...  and dependencies, that has some desired properties.  ...  for constructing join trees for acyclic database schemes (Tarjan & Yannakakis, 1984) . (3) Let R be acyclic, let T be a join tree for R, and let (R i, Ri) be an edge of T.  ... 
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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;
There is an analogy between degrees of acyclicity for database schemes and normal forms [ 15, 20] for relation schemata (a relation scheme along with its set of dependencies [21] ).  ...  However, unlike the situation for ordinary, undirected graphs, there are several natural, noneqmvalent notions of acyclicity for hypergraphs (and hence for database schemes).  ...  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.  ... 
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A view of directions in relational database theory [chapter]

Jeffrey D. Ullman
<span title="">1981</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;
These directions include dependency inferences, support for the universal relation concept, null value semantics, and an exploration of the properties of acyclic database schemes. I.  ...  It is the dependencies, such as functional and multivalued dependencies, that we assume about "legal" relations over that scheme, that cause redundancy.  ...  A join dependency is logically equivalent to a set of MVD's if and only if it is acyclic [FMUI. 2.  ... 
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On the Desirability of Acyclic Database Schemes

Catriel Beeri, Ronald Fagin, David Maier, Mihalis Yannakakis
<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;
Also given are several eqmvalent characterizations of those sets M of multivalued dependencies such that M is the set of muRlvalued dependencies that are the consequences of a given join dependency.  ...  In addition, several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given, and a smaple algorithm for determining acychclty is presented.  ...  The authors are grateful to Marc Graham, Maria Klawe, Jeff Ullman, Moshe Vardi, and Carlo Zaniolo for helpful comments.  ... 
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Pairwise-definable subdirect decompositions of general database schemata [chapter]

Stephen J. Hegner
<span title="">1991</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;
simplicity of constraints, correctness of query evaluation algorithms, and complexity of integrity maintenance.  ...  One of the most important results in the theory of decomposition of universal relational schemata is the equivalence of acyclicity of the hypergraph of the schema to numerous desirable properties regarding  ...  into projections and join dependencies, as recaptured by the following.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-54009-1_18">doi:10.1007/3-540-54009-1_18</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bselxpzfgfdxzmtcldx2pvzumq">fatcat:bselxpzfgfdxzmtcldx2pvzumq</a> </span>
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A simplied universal relation assumption and its properties

Ronald Fagin, Alberto O. Mendelzon, Jeffrey D. Ullman
<span title="1982-09-01">1982</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ahla23r2jva2bp2hlkt5rtbx4y" style="color: black;">ACM Transactions on Database Systems</a> </i> &nbsp;
We propose a simpler method of describing the real world, where constraints are given by functional dependencies and a single join dependency.  ...  We characterize in terms of hypergrapbs those multivalued dependencies that are the consequence of a given join dependency.  ...  ACKNOWLEDGMENTS The authors are grateful to Catriel Beeri, Maria Klawe, David Maier, and Moshe Vardi for useful suggestions.  ... 
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On the implication problem for probabilistic conditional independency

S.K.M. Wong, C.J. Butz, D. Wu
<span title="">2000</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/btdqpygqjnhzfe7tkrxo77bitm" style="color: black;">IEEE transactions on systems, man and cybernetics. Part A. Systems and humans</a> </i> &nbsp;
Index Terms-Bayesian networks, embedded multivalued dependency, implication problem, probabilistic conditional independence, relational databases.  ...  This means there is no real difference between Bayesian networks and relational databases, in the sense that only solvable classes of independencies are useful in the design and implementation of these  ...  The projection and natural join operations in relational databases are special cases of the marginalization and multiplication operations.  ... 
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Contributions to Logical Database Design

Vitalie COTELEA
<span title="">2012</span> <i title="Inforec Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lmfo33l5fnd6hpja5rybf7qc5a" style="color: black;">Informatică economică</a> </i> &nbsp;
It also summarizes and compares the different features of recognition of acyclic database schemas.  ...  This paper treats the problems arising at the stage of logical database design.  ...  the join dependency.  ... 
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Project-Join-Repair: An Approach to Consistent Query Answering Under Functional Dependencies [chapter]

Jef Wijsen
<span title="">2006</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;
Project-Join-Repair Σ = set of fd's σ = join dependency (jd) I = possibly inconsistent relation We repair σ(I)-rather than I. Note that σ(I) ⊇ I. We require Σ |= σ.  ...  R 2 Name Birth Sex ZIP City Ed 1962 M 7000 Bergen Project-Join-Repair (Example) Before repairing, apply the project-join dependency σ = [{Name, Birth, Sex, ZIP}, {ZIP, City}] : I Name Birth Sex  ...  Conclusion Database repairing and consistent query answering under fd's.  ... 
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Characterization of desirable properties of general database decompositions

Stephen J. Hegner
<span title="">1993</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/j2td7x4trvgx7pjoienrccryxq" style="color: black;">Annals of Mathematics and Artificial Intelligence</a> </i> &nbsp;
, and in turn equivalent to certain acyclicity characterizations of a hypergraph underlying the schema.  ...  Particularly, the classical notions of "pairwise consistency implies global consistency" and "hypergraph acyclicity" are not equivalent in the general case, but rather are independent of each other, and  ...  The author owes a special debt of gratitude to Ron Fagin, who gave the initial version of this paper a thorough reading and made numerous suggestions to improve the presentation. References  ... 
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A Formal Context for Acyclic Join Dependencies [chapter]

Jaume Baixeries
<span title="">2017</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;
Acyclic Join Dependencies (AJD) play a crucial role in database design and normalization.  ...  This present work simplifies and generalizes the characterization of Multivalued Dependencies with FCA.  ...  This research work has been supported by the SGR2014-890 (MACDA) project of the Generalitat de Catalunya, and MINECO project APCOM (TIN2014-57226-P).  ... 
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Page 424 of Mathematical Reviews Vol. , Issue 87a [page]

<span title="">1987</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;
In particular, a database schema B, de- scribed by one full join dependency and a set of functional depen- dencies, is represented by a (database) hypergraph H, containing both undirected and directed  ...  Author summary: “We consider the problem of optimizing al- gebraic queries in relational databases, which are formulated via inequality selection, projection, and natural join.  ... 
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Cycle structure of edge labelled graphs

James S. Diamond, Alberto O. Mendelzon
<span title="">1993</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;
As an application to relational database theory, we show how this algorithm can be combined with a new characterization of database acyclicity to determine the cyclicity of a relational database scheme  ...  We also give an efficient algorithm to determine whether or not the resulting graph is acyclic.  ...  Acknowledgement We would like to thank Lorna Stewart for a careful reading of the paper, and Derek Corneil, Kent Laver and Eric Mendelsohn for many useful discussions.  ... 
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