D. Suciu, J. Paredaens, Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure, in "Proceedings of 13th ACM Symposium on Principles of Database Systems," Minneapolis, May 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....coherence and consistency. Fifth, we allow for interval probabilities over solution sets of temporal constraints, while their work allows only for precise point probabilities over intervals of time points. Our work is also related to data models and algebraic operations for complex objects [1, 37, 44, 41, 40, 6]. Our work is a strict extension of the algebra for complex values presented by Abiteboul et al. 1] As in the case of Shaw and Zdonik [37] Vandenberg and DeWitt [44] and Boncz et al. 6] our data model supports the type constructors for sets and tuples on elementary datatypes. Like them, we ....

....in [6] and aggregate operations and next unnest operations. Of course, our work involves time and probabilities that are not considered in these papers. Extending our work to such types and algebraic operations is an interesting topic of future research. The nested relational algebra described in [41] is a functional language for complex objects, which also allows for defining the high level algebraic operations of selection, projection, Cartesian product, intersection, and difference [41] Finally, Subramanian et al. 40] describe an object oriented query algebra for lists and trees. They ....

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D. Suciu and J. Paredaens. Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure. In Proceedings PODS-94, pages 201--209. ACM Press, 1994.

....[AKRW92] These approaches seem to lead to a very inefficient use of space. In this paper, we present techniques for avoiding (or at least limiting) waste of space in the complex value algebra, calculus, and method schema frameworks. In the complex value algebra, we reconsider a nice result of [SP94] that states that any algebraic query expressing transitive closure essentially requires exponential space if evaluated naturally. We exhibit an evaluation technique that allows to compute a large class of queries (including TC) using only polynomial space. For such queries, we avoid computing ....

....expression filtering the relations that contain R and are closed transitively. The operator T takes the intersection of the relations that passed the test. Observe that this construction requires by essence exponential space in the database size because of powerset. Indeed, in a recent paper [SP94], it is shown that any expression in ALG cv needs exponential space to compute transitive closure. Now, let us examine this statement more closely. There is a basic assumption underlying it: expressions are evaluated in the natural manner; and for this particular style of evaluation, TC ....

D. Suciu and J. Paredaens. Any Algorithm in the Complex Object Algebra with Powerset Needs Exponential Space to Compute Transitive Closure. In Proc. 13th ACM Symposium on Principles of Database Systems, pp. 201--209, 1994.

....recursive queries such as transitive closure (tc) LW94] A B can express tc by first producing all possible relations on a given set of nodes and then selecting those that contain a given one and are transitive. Of course this way of computing tc uses exponential space. A remarkable result of [SP94] says that no matter how we write an A B expression to compute tc, it will use exponential space. However, it is based on a contrived restriction that a natural evaluation strategy is used. If this restriction is dropped, then it is possible to devise an evaluation strategy that computes tc in ....

D. Suciu and J. Paredaens. Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure. In PODS-94, pages 201--109. 230

....of the first and second projections of R, takes powerset of cartesian product of the domain with itself and then selects all elements from this powerset which are transitive and contain R. The intersection of those elements is the transitive closure of R. Moreover, Paredaens and Suciu showed [52] that any algorithm for computing transitive closure in NRL(powerset ) evaluated under the standard operational semantics, must use exponential space. Even though different evaluation schemes proposed recently [2, 33] give polynomial space algorithms for transitive closure in the powerset ....

D. Suciu, J. Paredaens, Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure, in "Proceedings of 13th ACM Symposium on Principles of Database Systems," Minneapolis, May 1994.

....potentially costly excursion through a powerset. This observation, made in [9] begs the question: is there an efficient way of programming these queries in A B This is a delicate question since it depends on accepting a reasonable notion of operational semantics for A B. Suciu and Paredaens [54] show that if we adopt the usual, eager, evaluation strategy for queries, then any A B expression for transitive closure must construct an intermediate result of exponential size, hence obtaining an EXPSPACE lower bound. Abiteboul and Hillebrand [2] show that an operational semantics with ....

....expressiveness in presence of aggregate functions and certain generic queries. Other results on expressive power are to be found in [34, 36, 35] Our approach can be used for different collections: languages for or sets were studied in [33, 23, 38] and bag languages in [37] As mentioned before, [54] shows that transitive closure, which is efficiently expressible using structural recursion, has a necessarily exponential implementation in complex object algebra [1] 30] show how to encode related database languages in the simply typed lambda calculus. The possibility of treating arrays as ....

D. Suciu, J. Paredaens, Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure, in "Proceedings of 13th ACM Symposium on Principles of Database Systems," 201--209, Minneapolis, May 1994.

....of [AKRW92] These approaches seem to lead to a very inefficient use of space. In this paper, we present techniques for avoiding (or at least limiting) waste of space in the complex value algebra, calculus, and method schema frameworks. In the complex value algebra, we reconsider a nice result of [SP94] that states that any algebraic query expressing transitive closure essentially requires exponential space if evaluated naturally. We exhibit an evaluation technique that allows to compute a large class of queries (including TC) using only polynomial space. For such queries, we avoid computing ....

....expression filtering the relations that contain R and are closed transitively. The operator T takes the intersection of the relations that passed the test. Observe that this construction requires by essence exponential space in the database size because of powerset. Indeed, in a recent paper [SP94], it is shown that any expression in ALG cv needs exponential space to compute transitive closure. Now, let us examine this statement more closely. There is a basic assumption underlying it: expressions are evaluated in the natural manner; and for this particular style of evaluation, TC ....

D. Suciu and J. Paredaens. Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure. In Proc. 13th ACM Symposium on Principles of Database Systems, pp. 201--209, 1994.

....and BALG powerbag was studied in [GM93] However, there are serious problems with the powerset. While all queries in Corollary 5.3 become definable, they are not definable efficiently. That is, under the natural evaluation strategy, computing transitive closure would require exponential space [SP94]. Even though more advanced query evaluation techniques proposed in [AH95, Lib95a] reduce this to polynomial space, it is unknown whether the exponential time complexity bound can be improved. Another way of enriching the language is adding the structural recursion operator to it. This was done ....

D. Suciu and J. Paredaens. Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure. In Proc. 13th ACM Symp. on Principles of Database Systems, 1994.

....exponential space. Results of similar flavor are obtained in [Yan86] for queries in the weak universal relation model. Lower bounds for expressing certain queries in Datalog are shown in [Afr94] Exponential lower bounds for expressing transitive closure in a complex value algebra are shown in [SP94] 20 VICTOR VIANU 5. The Frontier: New Applications, New Models Most of the discussion so far was set within the classical relational database framework. In recent years, the database field has gone beyond the classical framework, bringing into play a combination of formalisms and tools from ....

D. Suciu and J. Paredaens, Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure, Proc. ACM Symp. on Principles of Database Systems, 1994, pp. 171--179.

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D. Suciu, J. Paredaens, Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure, in "Proceedings of 13th ACM Symposium on Principles of Database Systems," Minneapolis, May 1994.

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D. Suciu and J. Paredaens. Any algorithm in the complex object algebra with powerset needs exponential space to compute transitive closure. In Proc. ACM Symp. on Principles of Database Systems, pages 171--179, 1994. BIBLIOGRAPHY 39

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