Testing implications of data dependencies
ACM Transactions on Database Systems (TODS)
Data integration: a theoretical perspective
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Generic Model Management: Concepts And Algorithms (Lecture Notes in Computer Science)
Generic Model Management: Concepts And Algorithms (Lecture Notes in Computer Science)
Schema mappings, data exchange, and metadata management
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Data exchange: semantics and query answering
Theoretical Computer Science - Database theory
Composing schema mappings: Second-order dependencies to the rescue
ACM Transactions on Database Systems (TODS) - Special Issue: SIGMOD/PODS 2004
Composition of mappings given by embedded dependencies
ACM Transactions on Database Systems (TODS)
Model management 2.0: manipulating richer mappings
Proceedings of the 2007 ACM SIGMOD international conference on Management of data
ACM Transactions on Database Systems (TODS)
Composing mappings among data sources
VLDB '03 Proceedings of the 29th international conference on Very large data bases - Volume 29
Quasi-inverses of schema mappings
ACM Transactions on Database Systems (TODS)
Reverse data exchange: coping with nulls
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The recovery of a schema mapping: Bringing exchanged data back
ACM Transactions on Database Systems (TODS)
Reverse data exchange: Coping with nulls
ACM Transactions on Database Systems (TODS)
Tiresias: the database oracle for how-to queries
SIGMOD '12 Proceedings of the 2012 ACM SIGMOD International Conference on Management of Data
Query language-based inverses of schema mappings: semantics, computation, and closure properties
The VLDB Journal — The International Journal on Very Large Data Bases
The language of plain SO-tgds: Composition, inversion and structural properties
Journal of Computer and System Sciences
Getting unique solution in data exchange
Proceedings of the VLDB Endowment
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A schema mapping is a specification that describes how data structured under one schema (the source schema) is to be transformed into data structured under a different schema (the target schema). The notion of an inverse of a schema mapping is subtle, because a schema mapping may associate many target instances with each source instance, and many source instances with each target instance. In PODS 2006, Fagin defined a notion of the inverse of a schema mapping. This notion is tailored to the types of schema mappings that commonly arise in practice (those specified by “source-to-target tuple-generating dependencies”, or s-t tgds). We resolve the key open problem of the complexity of deciding whether there is an inverse. We also explore a number of interesting questions, including: What is the structure of an inverse? When is the inverse unique? How many nonequivalent inverses can there be? When does an inverse have an inverse? How big must an inverse be? Surprisingly, these questions are all interrelated. We show that for schema mappings M specified by full s-t tgds (those with no existential quantifiers), if M has an inverse, then it has a polynomial-size inverse of a particularly nice form, and there is a polynomial-time algorithm for generating it. We introduce the notion of “essential conjunctions” (or “essential atoms” in the full case), and show that they play a crucial role in the study of inverses. We use them to give greatly simplified proofs of some known results about inverses. What emerges is a much deeper understanding about this fundamental and complex operator.