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18
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 ..."
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Cited by 17 (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
Dynamic tree isomorphism via firstorder updates
 In: PODS, ACM Press
, 1998
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Incremental query evaluation in a ring of databases
 In International Symposium on Principles of Database Systems (PODS
"... This paper approaches the incremental view maintenance problem from an algebraic perspective. We construct a ring of databases and use it as the foundation of the design of a query calculus that allows to express powerful aggregate queries. The query calculus inherits key properties of the ring, suc ..."
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Cited by 15 (4 self)
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This paper approaches the incremental view maintenance problem from an algebraic perspective. We construct a ring of databases and use it as the foundation of the design of a query calculus that allows to express powerful aggregate queries. The query calculus inherits key properties of the ring, such as having a normal form of polynomials and being closed under computing inverses and delta queries. The kth delta of a polynomial query of degree k without nesting is purely a function of the update, not of the database. This gives rise to a method of eliminating expensive query operators such as joins from programs that perform incremental view maintenance. The main result is that, for nonnested queries, each individual aggregate value can be incrementally maintained using a constant amount of work. This is not possible for nonincremental evaluation.
Incremental XPath Evaluation
"... We study the problem of incrementally maintaining the result of an XPath query on an XML database under updates. In its most general form, this problem asks to maintain a materialized XPath view over an XML database. It assumes an underlying XML database D and a query Q. One is given a sequence of u ..."
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We study the problem of incrementally maintaining the result of an XPath query on an XML database under updates. In its most general form, this problem asks to maintain a materialized XPath view over an XML database. It assumes an underlying XML database D and a query Q. One is given a sequence of updates U to D and the problem is to compute the result of Q(U(D)), i.e., the result of evaluating query Q on the database D after having applied the updates U. In order to quickly answer this question, we are allowed to maintain an auxiliary data structure, and the complexity of the maintenance algorithms is measured in (i) the size of the auxiliary data structure, (ii) the worstcase time per update needed to compute Q(U(D)) and (iii) the worstcase time per update needed to bring the auxiliary data structure up to date. We allow three kinds of updates: node insertion, node deletion, and node relabeling. Our main results are that downward XPath queries can be incrementally maintained in time O(depth(D) · poly(Q)) per update and conjunctive forward XPath queries in time O(depth(D)·log(width(D))·poly(Q)) per update, where Q  is the size of the query, and depth(D) and width(D) are the nesting depth and maximum number of siblings in the database D, respectively. The auxiliary data structures for maintenance are linear in D  and polynomial in Q  in all these cases.
Incremental Recomputation in Local Languages
 INFCTRL: Information and Computation (formerly Information and Control
, 2001
"... We study the problem of maintaining recursivelydened views, such as the transitive closure of a relation, in traditional relational languages that do not have recursion mechanisms. The main results of this paper are negative ones: we show that a certain property of query languages implies imposs ..."
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Cited by 9 (0 self)
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We study the problem of maintaining recursivelydened views, such as the transitive closure of a relation, in traditional relational languages that do not have recursion mechanisms. The main results of this paper are negative ones: we show that a certain property of query languages implies impossibility of such incremental maintenance. The property we use is locality of queries, which is known to hold for relational calculus and various extensions, including those with grouping and aggregate constructs (essentially, plain SQL). 1
Abstract Interpretation for Termination Analysis in Functional Active Databases
 JIIS
, 1999
"... An active database consists of a traditional database supplemented by a set of EventConditionAction (ECA) rules. One of the key questions for active database designers is that of termination of the ECA rules. The behaviour of the ECA rules may be obscure and their semantics is often not specifie ..."
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Cited by 8 (3 self)
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An active database consists of a traditional database supplemented by a set of EventConditionAction (ECA) rules. One of the key questions for active database designers is that of termination of the ECA rules. The behaviour of the ECA rules may be obscure and their semantics is often not specified formally. Consequently, developing termination analysis algorithms and proving their correctness is a challenging task. In this paper we address this problem for functional active databases by adopting an abstract interpretation approach. By "functional active databases" we mean active databases whose transaction execution semantics have been expressed in a purely functional language. Although we demonstrate our tech...
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 8 (2 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
The Dynamic Complexity of Transitive Closure is in DynTC0
 In Proceedings of the 8th International Conference on Database Theory (2001
, 2002
"... This paper presents a fully dynamic algorithm for maintaining the transitive closure of a binary relation. All updates and queries can be computed by constant depth threshold circuits of polynomial size (TC circuits). This places dynamic transitive closure in the dynamic complexity class DynTC ..."
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This paper presents a fully dynamic algorithm for maintaining the transitive closure of a binary relation. All updates and queries can be computed by constant depth threshold circuits of polynomial size (TC circuits). This places dynamic transitive closure in the dynamic complexity class DynTC , and implies that transitive closure can be maintained in database systems that include firstorder update queries and aggregation operators, using a database with size polynomial in the size of the relation.
Dynamic Complexity Theory Revisited
 Proc. Annual Symposium on Theoretical Aspects of Computer Science (STACS 05), Springer LNCS 3404, 2005
, 2005
"... Abstract. Dynamic complexity asks for the effort needed to maintain the information about properties of a structure under operations changing the structure. This paper introduces a refined notion of dynamic problems which takes the initial structure into account. It develops the basic structural com ..."
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Abstract. Dynamic complexity asks for the effort needed to maintain the information about properties of a structure under operations changing the structure. This paper introduces a refined notion of dynamic problems which takes the initial structure into account. It develops the basic structural complexity notions accordingly. It also shows that the dynamic version of the LOGCFLcomplete problem D2LREACH(acyclic) can be maintained with firstorder updates. 1