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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

1992
*
Data & Knowledge Engineering
*

In this paper we describe an optimization strategy that rewrites regular (in

doi:10.1016/0169-023x(92)90029-b
fatcat:tcydmhdf6zcgri3ty3dmhgmd5i
*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. ...##
###
A survey of parallel execution strategies for transitive closure and logic programs

1993
*
Distributed and parallel databases
*

We first analyze

doi:10.1007/bf01264013
fatcat:pe4vicsr3vctzoj437towrkdv4
*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. ...##
###
The dynamic complexity of transitive closure is in DynTC0

2003
*
Theoretical Computer Science
*

This paper presents

doi:10.1016/s0304-3975(02)00740-5
fatcat:jcdbk7gt5bejjk25v3dpefnm4a
*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*. ...##
###
Point-based approaches to qualitative temporal reasoning
[chapter]

1998
*
Lecture Notes in Computer Science
*

We consider general reasoners tailored for temporal domains that exhibit

doi:10.1007/bfb0095279
fatcat:ra7zhqhxoban5e2zx6jna3sg3u
*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 ...##
###
Sub-Computation Based Transition Predicate Abstraction

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*. ...

##
###
A query language for NC

1994
*
Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '94
*

We show that

doi:10.1145/182591.182610
dblp:conf/pods/SuciuT94
fatcat:m7dnxxsxcnfnpfhkk4act5yfbu
*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 ...##
###
Low complexity aggregation in graphlog and Datalog
[chapter]

1990
*
Lecture Notes in Computer Science
*

We present constructs for

doi:10.1007/3-540-53507-1_90
fatcat:2g6qdn6z6zdvzaenawkarx5rtq
*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. ...##
###
Low-complexity aggregation in GraphLog and Datalog

1993
*
Theoretical Computer Science
*

Acknowledgment We are indebted to Isabel Cruz for fruitful discussions and Steve Cook for his help with

doi:10.1016/0304-3975(93)90221-e
fatcat:27x3ed2f7baktmumyfcvxuwntq
*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. ...##
###
Complex transitive closure queries on a fragmented graph
[chapter]

1990
*
Lecture Notes in Computer Science
*

We view

doi:10.1007/3-540-53507-1_96
fatcat:y7ucgrmwxzd7vjuxqjaso2moqm
*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*. ...##
###
Incremental maintenance of recursive views using relational calculus/SQL

2000
*
SIGMOD record
*

Very often

doi:10.1145/344788.344808
fatcat:skqbr5qkmzg55gla3fpbpy7h4u
*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. ...##
###
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

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. ...

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