ABSTRACT
Over the past several decades, the study of conjunctive queries has occupied a central place in the theory and practice of database systems. In recent years, conjunctive queries have played a prominent role in the design and use of schema mappings for data integration and data exchange tasks. In this paper, we investigate several different aspects of conjunctive-query equivalence in the context of schema mappings and data exchange.
In the first part of the paper, we introduce and study a notion of a local transformation between database instances that is based on conjunctive-query equivalence. We show that the chase procedure for GLAV mappings (that is, schema mappings specified by source-to-target tuple-generating dependencies) is a local transformation with respect to conjunctive-query equivalence. This means that the chase procedure preserves bounded conjunctive-query equivalence, that is, if two source instances are indistinguishable using conjunctive queries of a sufficiently large size, then the target instances obtained by chasing these two source instances are also indistinguishable using conjunctive queries of a given size. Moreover, we obtain polynomial bounds on the level of indistinguishability between source instances needed to guarantee indistinguishability between the target instances produced by the chase. The locality of the chase extends to schema mappings specified by a second-order tuple-generating dependency (SO tgd), but does not hold for schema mappings whose specification includes target constraints.
In the second part of the paper, we take a closer look at the composition of two GLAV mappings. In particular, we break GLAV mappings into a small number of well-studied classes (including LAV and GAV), and complete the picture as to when the composition of schema mappings from these various classes can be guaranteed to be a GLAV mapping, and when they can be guaranteed to be conjunctive-query equivalent to a GLAV mapping.
We also show that the following problem is decidable: given a schema mapping specified by an SO tgd and a GLAV mapping, are they conjunctive-query equivalent? In contrast, the following problem is known to be undecidable: given a schema mapping specified by an SO tgd and a GLAV mapping, are they logically equivalent?
- M. Arenas, P. Barceló, R. Fagin, and L. Libkin. Locally consistent transformations and query answering in data exchange. In ACM Symp. on Principles of Database Systems, pages 229--240, 2004. Google Scholar
Digital Library
- M. Arenas, P. Barceló, L. Libkin, and F. Murlak. Relational and XML Data Exchange. Synthesis Lectures on Data Management. Morgan & Claypool Publishers, 2010. Google Scholar
Digital Library
- A. V. Aho, C. Beeri, and J. D. Ullman. The theory of joins in relational databases. ACM Trans. on Database Systems, 4(3):297--314, 1979. Google Scholar
Digital Library
- P.C. Arocena, A. Fuxman, and R.J. Miller. Composing local-as-view mappings: closure and applications. In Int. Conf. on Database Theory, pages 209--218, 2010. Google Scholar
Digital Library
- M. Arenas, R. Fagin, and A. Nash. Composition with target constraints. Logical Methods in Computer Science, 7(3:13):1--38, 2011.Google Scholar
- M. Arenas, J. Pérez, and C. Riveros. The recovery of a schema mapping: Bringing exchanged data back. ACM Trans. on Database Systems, 34(4), 2009. Google Scholar
Digital Library
- M. Arenas, J. Pérez, J.L. Reutter, and C. Riveros. Inverting schema mappings: Bridging the gap between theory and practice. PVLDB, 2(1):1018--1029, 2009. Google Scholar
Digital Library
- A. K. Chandra and P. M. Merlin. Optimal implementation of conjunctive queries in relational data bases. In ACM Symp. on Theory of Computing, pages 77--90, 1977. Google Scholar
Digital Library
- R. Fagin. Inverting schema mappings. ACM Trans. on Database Systems, 32(4), 2007. Google Scholar
Digital Library
- R. Fagin, P. G. Kolaitis, R. J. Miller, and L. Popa. Data exchange: Semantics and query answering. Theoretical Computer Science, 336(1):89--124, 2005. Google Scholar
Digital Library
- R. Fagin, P. G. Kolaitis, A. Nash, and L. Popa. Towards a theory of schema-mapping optimization. In ACM Symp. on Principles of Database Systems, pages 33--42, 2008. Google Scholar
Digital Library
- R. Fagin, P. G. Kolaitis, L. Popa, and W.-C. Tan. Composing schema mappings: Second-order dependencies to the rescue. ACM Trans. on Database Systems, 30(4):994--1055, 2005. Google Scholar
Digital Library
- R. Fagin, P.G. Kolaitis, L. Popa, and W-C. Tan. Schema mapping evolution through composition and inversion. In Z. Bellahsene, A. Bonifati, and E. Rahm, editors, Schema Matching and Mapping, pages 191--222. Springer, 2011.Google Scholar
Cross Ref
- I. Feinerer, R. Pichler, E. Sallinger, and V. Savenkov. On the undecidability of the equivalence of second-order tuple generating dependencies. In Alberto Mendelzon Workshop, 2011.Google Scholar
- R. Fagin, L. Stockmeyer, and M. Y. Vardi. On monadic NP vs. monadic co-NP. Inf. and Computation, 120(1):78--92, July 1995. Google Scholar
Digital Library
- P. Hell and J. Nešetvřil. The core of a graph. Discrete Mathematics, 109:117--126, 1992. Google Scholar
Digital Library
- P. G. Kolaitis. Schema mappings, data exchange, and metadata management. In ACM Symp. on Principles of Database Systems, pages 61--75, 2005. Google Scholar
Digital Library
- M. Lenzerini. Data integration: A theoretical perspective. In ACM Symp. on Principles of Database Systems, pages 233--246, 2002. Google Scholar
Digital Library
- J. Madhavan and A. Y. Halevy. Composing mappings among data sources. In Int. Conf. on Very Large Data Bases, pages 572--583, 2003. Google Scholar
Digital Library
- D. Maier, A. O. Mendelzon, and Y. Sagiv. Testing implications of data dependencies. ACM Trans. on Database Systems, 4(4):455--469, 1979. Google Scholar
Digital Library
- J. Nešetvřil and P. Ossona de Mendez. From sparse graphs to nowhere dense structures: Decompositions, independence, dualities and limits. In Proc. of the Fifth European Congress of Mathematics, 2009.Google Scholar
- R. Pichler, E. Sallinger, and V. Savenkov. Relaxed notions of schema mapping equivalence revisited. In Int. Conf. on Database Theory, pages 90--101, 2011. Google Scholar
Digital Library
- B. Rossman. Homomorphism preservation theorems. J. ACM, 55(3), 2008. Google Scholar
Digital Library
Index Terms
Local transformations and conjunctive-query equivalence
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