Generalized schema-mappings: from termination to tractability

Data-Exchange is the problem of creating new databases according to a high-level specification called a schema-mapping while preserving the information encoded in a source database. This paper introduces a notion of generalized schema-mapping that enriches the standard schema-mappings (as defined by Fagin et al) with more expressive power. It then proposes a more general and arguably more intuitive notion of semantics that rely on three criteria: Soundness, Completeness and Laconicity (non-redundancy and minimal size). These semantics are shown to coincide precisely with the notion of cores of universal solutions in the framework of Fagin, Kolaitis and Popa. It is also well-defined and of interest for larger classes of schema-mappings and more expressive source databases (with null-values and equality constraints). After an investigation of the key properties of generalized schema-mappings and their semantics, a criterion called Termination of the Oblivious Chase (TOC) is identified that ensures polynomial data-complexity. This criterion strictly generalizes the previously known criterion of Weak-Acyclicity. To prove the tractability of TOC schema-mappings, a new polynomial time algorithm is provided that, unlike the algorithm of Gottlob and Nash from which it is inspired, does not rely on the syntactic property of Weak-Acyclicity. As the problem of deciding whether a Schema-mapping satisfies the TOC criterion is only recursively enumerable, a more restrictive criterion called Super-weak Acylicity (SwA) is identified that can be decided in Polynomial-time while generalizing substantially the notion of Weak-Acyclicity.