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Incremental Maintenance of Recursive Views Using Relational Calculus/SQL
 SIGMOD Record
, 2000
"... Views are a central component of both traditional database systems and new applications such as data warehouses. Very often the desired views (e.g. the transitive closure) cannot be defined in the standard language of the underlying database system. Fortunately, it is often possible to incrementall ..."
Abstract

Cited by 15 (1 self)
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Views are a central component of both traditional database systems and new applications such as data warehouses. Very often the desired views (e.g. the transitive closure) cannot be defined in the standard language of the underlying database system. Fortunately, it is often possible to incrementally maintain these views using the standard language. For example, transitive closure of acyclic graphs, and of undirected graphs, can be maintained in relational calculus after both single edge insertions and deletions. Many such results have been published in the theoretical database community. The purpose of this survey is to make these useful results known to the wider database research and development community. There are many interesting issues involved in the maintenance of recursive views. A maintenance algorithm may be applicable to just one view, or to a class of views specified by a view definition language such as Datalog. The maintenance algorithm can be specified in a maintenance language of different expressiveness, such as the conjunctive queries, the relational calculus or SQL. Ideally, this maintenance language should be less expensive than the view definition language. The maintenance algorithm may allow updates of different kinds, such as just single tuple insertions, just single tuple deletions, special setbased insertions and/or deletions, or combinations thereof. The view maintenance algorithms may also need to maintain auxiliary relations to help maintain the views of interest. It is of interest to know the minimal arity necessary for these auxiliary relations
Maintaining the transitive closure of graphs in SQL
 In Int. J. Information Technology
, 1999
"... It is common knowledge that relational calculus and even SQL are not expressive enough to express recursive queries such as the transitive closure. In a real database system, one can overcome this problem by storing a graph together with its transitive closure and maintaining the latter whenever upd ..."
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Cited by 7 (3 self)
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It is common knowledge that relational calculus and even SQL are not expressive enough to express recursive queries such as the transitive closure. In a real database system, one can overcome this problem by storing a graph together with its transitive closure and maintaining the latter whenever updates to the former occur. This leads to the concept of an incremental evaluation system, or IES. Much is already known about the theory of IES but very little has been translated into practice. The purpose of this paper is to ll in this gap by providing a gentle introduction to and an overview of some recent theoretical results on IES. The introduction is through the translation into SQL of three interesting positive maintenance results that have practical importance { the maintenance of the transitive closure of acyclic graphs, of undirected graphs, and of arbitrary directed graphs. Interestingly, these examples also allow ustoshow the relationship between power and cost in the incremental maintenance of database queries. 1
Incremental maintenance of shortest distance and transitive closure in firstorder logic and sql
 ACM Trans. Database Syst
"... Given a database, the view maintenance problem is concerned with the efficient computation of the new contents of a given view when updates to the database happen. We consider the view maintenance problem for the situation when the database contains a (weighted) graph and the view is either the tran ..."
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Cited by 6 (2 self)
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Given a database, the view maintenance problem is concerned with the efficient computation of the new contents of a given view when updates to the database happen. We consider the view maintenance problem for the situation when the database contains a (weighted) graph and the view is either the transitive closure or the answer to the allpairs shortestdistance problem (APSD). We give incremental algorithms for (APSD), which support both edge insertions and deletions. For transitive closure, the algorithm is applicable to a more general class of graphs than those previously explored. Our algorithms use firstorder queries, along with addition (+) and lessthan (<) operations (F O(+, <)); they store O(n 2) number of tuples, where n is the number of vertices, and have AC 0 data complexity for integer weights. Since F O(+, <) is a sublanguage of SQL and is supported by almost all current database systems, our maintenance algorithms are more appropriate for database applications than nondatabase query type of maintenance algorithms.
Maintaining Transitive Closure of Graphs in SQL
 In Int. J. Information Technology
, 1999
"... It is common knowledge that relational calculus and even SQL are not expressive enough to express recursive queries such as the transitive closure. In a real database system, one can overcome this problem by storing a graph together with its transitive closure and maintaining the latter whenever ..."
Abstract
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It is common knowledge that relational calculus and even SQL are not expressive enough to express recursive queries such as the transitive closure. In a real database system, one can overcome this problem by storing a graph together with its transitive closure and maintaining the latter whenever updates to the former occur. This leads to the concept of an incremental evaluation system, or IES. Much is already known about the theory of IES but very little has been translated into practice. The purpose of this paper is to fill in this gap by providing a gentle introduction to and an overview of some recent theoretical results on IES. The introduction is through the translation into SQL of three interesting positive maintenance results that have practical importance  the maintenance of the transitive closure of acyclic graphs, of undirected graphs, and of arbitrary directed graphs. Interestingly, these examples also allow us to show the relationship between power and cost in ...