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Incremental Maintenance of Views with Duplicates
"... We study the problem of efficient maintenance of materialized views that may contain duplicates. This problem is particularly important when queries against such views involve aggregate functions, which need duplicates to produce correct results. Unlike most work on the view maintenance problem that ..."
Abstract

Cited by 164 (8 self)
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We study the problem of efficient maintenance of materialized views that may contain duplicates. This problem is particularly important when queries against such views involve aggregate functions, which need duplicates to produce correct results. Unlike most work on the view maintenance problem that is based on an algorithmic approach, our approach is algebraic and based on equational reasoning. This approach has a number of advantages: it is robust and easily extendible to new language constructs, it produces output that can be used by query optimizers, and it simpli es correctness proofs. We use a natural extension of the relational algebra operations to bags (multisets) as our basic language. We present an algorithm that propagates changes from base relations to materialized views. This algorithm is based on reasoning about equivalence of bagvalued expressions. We prove that it is correct and preserves a certain notion of minimality that ensures that no unnecessary tuples are computed. Although it is generally only a heuristic that computing changes to the view rather than recomputing the view from scratch is more efficient, we prove results saying that under normal circumstances one should expect the change propagation algorithm to be significantly faster and more space efficient than complete recomputing of the view. We also show that our approach interacts nicely with aggregate functions, allowing their correct evaluation on views that change.
Principles of Programming with Complex Objects and Collection Types
 Theoretical Computer Science
, 1995
"... We present a new principle for the development of database query languages that the primitive operations should be organized around types. Viewing a relational database as consisting of sets of records, this principle dictates that we should investigate separately operations for records and sets. Th ..."
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Cited by 128 (28 self)
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We present a new principle for the development of database query languages that the primitive operations should be organized around types. Viewing a relational database as consisting of sets of records, this principle dictates that we should investigate separately operations for records and sets. There are two immediate advantages of this approach, which is partly inspired by basic ideas from category theory. First, it provides a language for structures in which record and set types may be freely combined: nested relations or complex objects. Second, the fundamental operations for sets are closely related to those for other "collection types" such as bags or lists, and this suggests how database languages may be uniformly extended to these new types. The most general operation on sets, that of structural recursion, is one in which not all programs are welldefined. In looking for limited forms of this operation that always give rise to welldefined operations, we find a number of close ...
DomainIndependent Queries on Databases with External Functions
 in "LNCS 893: Proceedings of 5th International Conference on Database Theory," 177190
, 1995
"... We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with f ..."
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Cited by 13 (2 self)
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We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with fixpoints or other kinds of iterators. Next, we define two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our definition of computable queries with external functions is robust. Finally, based on the equivalence result, we give examples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over flat relations. 1 Introduction Database functionalities are important both for practical and for theoretical purposes. E.g. the system O 2 of ...
The Restricted and Bounded Fixpoint Closures of the Nested Algebra are Equivalent
 In Proceedings of DBPL'95
, 1995
"... The nested model is an extension of the traditional, "flat" relational model in which relations can also have relationvalued entries. Its "default" query language, the nested algebra, is rather weak, unfortunately, since it is only a conservative extension of the traditional, "flat" relational algeb ..."
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Cited by 4 (1 self)
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The nested model is an extension of the traditional, "flat" relational model in which relations can also have relationvalued entries. Its "default" query language, the nested algebra, is rather weak, unfortunately, since it is only a conservative extension of the traditional, "flat" relational algebra, and thus can only express a small fraction of the polynomialtime queries. Therefore, it was proposed to extend the nested algebra with a leastfixpoint construct, but the resulting language turned out to be too powerful: many inherently exponential queries could also be expressed. Two polynomialtime restrictions of the leastfixpoint closure of the nested algebra were proposed: the restricted leastfixpoint closure (by Gyssens and Van Gucht) and the bounded fixpoint closure (by Suciu). Here, we prove that both restrictions are equivalent in expressive power. We also exhibit a proof technique, called type substitution, by which we reduce our result to its obvious counterpart in the "fla...
Abstract Subset Queries in Relational Databases
"... In this paper, we motivated the need for relational database systems to support subset query processing. We defined new operators in relational algebra, and new constructs in SQL for expressing subset queries. We also illustrated the applicability of subset queries through different examples express ..."
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Cited by 1 (0 self)
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In this paper, we motivated the need for relational database systems to support subset query processing. We defined new operators in relational algebra, and new constructs in SQL for expressing subset queries. We also illustrated the applicability of subset queries through different examples expressed using extended SQL statements and relational algebra expressions. Our aim is to show the utility of subset queries for next generation applications. 1
Incremental Maintenance of Views with Duplicates
 In SIGMOD
, 1995
"... We study the problem of efficient maintenance of materialized views that may contain duplicates. This problem is particularly important when queries against such views involve aggregate functions, which need duplicates to produce correct results. Unlike most work on the view maintenance problem that ..."
Abstract
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We study the problem of efficient maintenance of materialized views that may contain duplicates. This problem is particularly important when queries against such views involve aggregate functions, which need duplicates to produce correct results. Unlike most work on the view maintenance problem that is based on an algorithmic approach, our approach is algebraic and based on equational reasoning. This approach has a number of advantages: it is robust and easily extendible to new language constructs, it produces output that can be used by query optimizers, and it simplifies correctness proofs. We use a natural extension of the relational algebra operations to bags (multisets) as our basic language. We present an algorithm that propagates changes from base relations to materialized views. This algorithm is based on reasoning about equivalence of bagvalued expressions. We prove that it is correct and preserves a certain notion of minimality that ensures that no unnecessary tuples are com...
Query Languages for Bags and Aggregate Functions
 Journal of Computer and System Sciences
, 1997
"... Theoretical foundations for querying databases based on bags are studied in this paper. We fully determine the strength of many polynomialtime bag operators relative to an ambient query language. Then we obtain BQL, a query language for bags, by picking the strongest combination of these operato ..."
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Theoretical foundations for querying databases based on bags are studied in this paper. We fully determine the strength of many polynomialtime bag operators relative to an ambient query language. Then we obtain BQL, a query language for bags, by picking the strongest combination of these operators. The relationship between the nested relational algebra and various fragments of BQL is investigated. The precise amount of extra power that BQL possesses over the nested relational algebra is determined. It is shown that the additional expressiveness of BQL amounts to adding aggregate functions to a relational language. The expressive power of BQL and related languages is investigated in depth. We prove that these languages possess the conservative extension property. That is, the expressibility of queries in these languages is independent of the nesting height of intermediate data. Using this result, we show that recursive queries, such as transitive closure, are not definable in...
Founded by Benjamin Franklin in 1740
, 1995
"... We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with x ..."
Abstract
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We investigate queries in the presence of external functions with arbitrary inputs and outputs (atomic values, sets, nested sets etc). We propose a new notion of domain independence for queries with external functions which, in contrast to previous work, can also be applied to query languages with xpoints or other kinds of iterators. Next, we de ne two new notions of computable queries with external functions, and prove that they are equivalent, under the assumption that the external functions are total. Thus, our de nition of computable queries with external functions is robust. Finally, based on the equivalence result, we giveexamples of complete query languages with external functions. A byproduct of the equivalence result is the fact that Relational Machines are complete for complex objects: it was known that they are not complete over at relations. 1
Chapter 10 Databases
"... This chapter is about database research (or as we abbreviate DBR). To people outside of computer science – and perhaps to many within – it will be unclear what this term means. First of all, what is a “database”? Used generally, it could mean any collection of information. It is obvious that there a ..."
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This chapter is about database research (or as we abbreviate DBR). To people outside of computer science – and perhaps to many within – it will be unclear what this term means. First of all, what is a “database”? Used generally, it could mean any collection of information. It is obvious that there are deep scientific issues involved in managing