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Page 1392 of Mathematical Reviews Vol. , Issue 2004b [page]

2004 Mathematical Reviews  
The present paper proves that when auxiliary relations are restricted to be unary (1.e., plain sets), transitive closure under deletions is in fact not maintainable in the relational calculus.  ...  For example, one can write a re- lational calculus query that takes as input a binary relation, its 68 COMPUTER SCIENCE 1392 current transitive closure, and a tuple to be added to the relation, and produces  ... 

Algebraic optimization of recursive queries

Maurice A.W. Houtsma, Peter M.G. Apers
1992 Data & Knowledge Engineering  
In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations  ...  We also describe how to push selections into the resulting transitive closure operations.  ...  Acknowledgements We thank the reviewers for their comments, which have greatly improved the quality of the paper.  ... 
doi:10.1016/0169-023x(92)90029-b fatcat:tcydmhdf6zcgri3ty3dmhgmd5i

A survey of parallel execution strategies for transitive closure and logic programs

Filippo Cacace, Stefano Ceri, Maurice Houtsma
1993 Distributed and parallel databases  
We first analyze the relationship between the transitive closure of expressions in Relational Algebra and Datalog programs.  ...  We observe that research on parallel execution of recursive queries is separated into two distinct subareas, one focused on the transitive closure of Relational Algebra expressions, the other one focused  ...  Stefano Ceri is partially supported by Esprit Project P6333, IDEA and the research of Maurice Houtsma has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.  ... 
doi:10.1007/bf01264013 fatcat:pe4vicsr3vctzoj437towrkdv4

The dynamic complexity of transitive closure is in DynTC0

William Hesse
2003 Theoretical Computer Science  
This paper presents a fully dynamic algorithm for maintaining the transitive closure of a binary relation.  ...  operators, using a database with size polynomial in the size of the relation.  ...  SQLIES that maintains the transitive closure of a binary relation.  ... 
doi:10.1016/s0304-3975(02)00740-5 fatcat:jcdbk7gt5bejjk25v3dpefnm4a

Point-based approaches to qualitative temporal reasoning [chapter]

T. Van Allen, J. Delgrande, A. Gupta
1998 Lecture Notes in Computer Science  
We consider general reasoners tailored for temporal domains that exhibit a particular structure and introduce such a reasoner based on the series-parallel graph reasoner of Delgrande and Gupta; this reasoner  ...  We address the general problem of finding algorithms for efficient, qualitative, point-based temporal reasoning over a set of operations.  ...  However, computing deductive closure on a set of point relation constraints is not a particularly efficient process because of axiom 7 (deductive closure is not transitive closure for temporally labeled  ... 
doi:10.1007/bfb0095279 fatcat:ra7zhqhxoban5e2zx6jna3sg3u

Sub-Computation Based Transition Predicate Abstraction

Carl Christian Frederiksen, Masami Hagiya
2007 IPSJ Digital Courier  
The transition predicate abstraction framework developed by Podelski, et al. (2005) captures size relations over state transitions which can be used to show infeasibility of certain program computations  ...  We present two versions of the sub-computation based analysis: one for a non-parallel imperative language with loops and recursive procedures, serving as an introduction, and one for the extension of the  ...  of the corresponding transition relations can be computed without restrictions on the domain of the transition relations.  ... 
doi:10.2197/ipsjdc.3.380 fatcat:kg4wt6xbj5dpvomb2jf5m7j44e

A query language for NC

Dan Suciu, Val Breazu-Tannen
1994 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '94  
We show that a form of divide and conquer recursion on sets together with the relational algebri expresses exactly the queries over ordered relational databases which are NCcomputable.  ...  At a finer level, we relate k nested uses of recursion exactly to A C~, k > 1. We also give corresponding results for complex objects.  ...  We thank Scott Weinstein for many illuminating discussions, Neil Immerman for answering our sometimes naive queries, Peter Buneman and Leonid Libkin for suggestions from a careful reading of an earlier  ... 
doi:10.1145/182591.182610 dblp:conf/pods/SuciuT94 fatcat:m7dnxxsxcnfnpfhkk4act5yfbu

Low complexity aggregation in graphlog and Datalog [chapter]

Mariano P. Consens, Alberto O. Mendelzon
1990 Lecture Notes in Computer Science  
We present constructs for computing aggregate functions over sets of tuples and along paths in a database graph.  ...  Our approach retains the standard relational notion of relations as sets of tuples, not requiring the introduction of multisets.  ...  Acknowledgments We are indebted to Isabel Cruz for fruitful discussions and Steve Cook for his help with the ner points of parallel complexity theory.  ... 
doi:10.1007/3-540-53507-1_90 fatcat:2g6qdn6z6zdvzaenawkarx5rtq

Low-complexity aggregation in GraphLog and Datalog

Mariano P. Consens, Alberto O. Mendelzon
1993 Theoretical Computer Science  
Acknowledgment We are indebted to Isabel Cruz for fruitful discussions and Steve Cook for his help with the finer points of parallel complexity theory.  ...  The closure literal contains+ represents the transitive closure of relation contains and appears labeling a dashed edge, a graphical notation that suggests that the edge in the query graph matches paths  ...  An edge of the query graph labeled with a closure literal s+ introduces an IDB predicate defined by additional rules expressing the transitive closure of the predicate in s.  ... 
doi:10.1016/0304-3975(93)90221-e fatcat:27x3ed2f7baktmumyfcvxuwntq

Complex transitive closure queries on a fragmented graph [chapter]

Maurice A. W. Houtsma, Peter M. G. Apers, Stefano Ceri
1990 Lecture Notes in Computer Science  
We view the study of distributed computation of transitive closure queries as a result of the trend towards distributed computation.  ...  First selections were distributed to fragments of a relation, then fragmentation was used to compute joins in a distributed way, and now we are studying distributed computation of transitive closure queries  ...  In a relational database context the use of distributed processing focuses on a special operation, viz. transitive closure.  ... 
doi:10.1007/3-540-53507-1_96 fatcat:y7ucgrmwxzd7vjuxqjaso2moqm

Incremental maintenance of recursive views using relational calculus/SQL

Guozhu Dong, Jianwen Su
2000 SIGMOD record  
Very often the desired views (e.g. the transitive closure) cannot be defined in the standard language of the underlying database system.  ...  For example, transitive closure of acyclic graphs, and of undirected graphs, can be maintained in relational calculus after both single edge insertions and deletions.  ...  Transitive closure of undirected graphs We now show how to maintain the transitive closure of undirected graphs in the relational calculus.  ... 
doi:10.1145/344788.344808 fatcat:skqbr5qkmzg55gla3fpbpy7h4u

Page 5723 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
[Wen, Zhaofang] (1-ODM) An efficient parallel algorithm for multiselection. Parallel Comput. 17 (1991), no. 6-7, 689-693. Summary: “The problem of multiselection arises frequently in databases.  ...  Using Ehrenfeucht-Fraissé games, the authors show that CALC; cannot express transitive closure of a graph whose nodes are objects with set nesting i. However, this may be expressed in CALC;,;.  ... 

Page 393 of Mathematical Reviews Vol. , Issue 93a [page]

1993 Mathematical Reviews  
On the other hand, the powerset algebra does allow the expression of transitive closure, but in a too expensive way.  ...  Summary: “The nested relational algebra is often inadequate as a tool to handle nested relations, since several important queries, such as transitive closure, cannot be expressed by it.  ... 

Page 5680 of Mathematical Reviews Vol. , Issue 93j [page]

1993 Mathematical Reviews  
computationally difficult because of the exponential size of the closure.  ...  Summary: “Since the normal forms 3NF, BCNF and 4NF are defined in terms of the closure of a set of dependencies, using the definitions directly to test if a relation scheme is in one of these forms is  ... 

Efficient parallel algorithms for functional dependency manipulations

Radhakrishnan Sridhar, Sitharama S. Iyengar
1990 Proceedings of the second international symposium on Databases in parallel and distributed systems - DPDS '90  
the number of arcs and nodes of the graph HE For graphs Hz with fixed degree and diameter, we show that the closure Hz+ can be computed in NC.  ...  The algorithms are efficient based on the transitive closure bottleneck phenomenon [7] that is, any improvement in the time and processor complexity of the transitive closure algorithm will result in an  ...  ACKNOWLEDGEMENTS We thank the anonymous refrees for their comments and Dr. Rakesh Agarwal for the prompt communications with respect to our submission to this conference.  ... 
doi:10.1145/319057.319078 fatcat:ixspdmcyn5ew5owjnqtdtluj34
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