Limits to parallel computation: P-completeness theory
Limits to parallel computation: P-completeness theory
Chasing constrained tuple-generating dependencies
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Theoretical Computer Science - Special issue: principles and practice of constraint programming
Complexity of answering queries using materialized views
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Constraint-generating dependencies
Journal of Computer and System Sciences
Reasoning with Disjunctive Constrained Tuple-Generating Dependencies
DEXA '01 Proceedings of the 12th International Conference on Database and Expert Systems Applications
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
On the Complexity of Numerical Analysis
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
ACM Transactions on Database Systems (TODS)
Data exchange in the presence of arithmetic comparisons
EDBT '08 Proceedings of the 11th international conference on Extending database technology: Advances in database technology
Real Algebraic Numbers: Complexity Analysis and Experimentation
Reliable Implementation of Real Number Algorithms: Theory and Practice
Laconic schema mappings: computing the core with SQL queries
Proceedings of the VLDB Endowment
Data exchange: On the complexity of answering queries with inequalities
Information Processing Letters
Relational and XML Data Exchange
Relational and XML Data Exchange
Designing and refining schema mappings via data examples
Proceedings of the 2011 ACM SIGMOD International Conference on Management of data
Complexity of some geometric and topological problems
GD'09 Proceedings of the 17th international conference on Graph Drawing
A sound and complete chase procedure for constrained tuple-generating dependencies
Journal of Intelligent Information Systems
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Data exchange is the problem of transforming data structured under a source schema into data structured under a target schema, taking into account structural relationships between the two schemas, which are described by a schema mapping. Existing schema-mapping languages lack the ability to express arithmetic operations, such as addition and multiplication, which naturally arise in data warehousing, ETL applications, and applications involving scientific data. We initiate the study of data exchange for arithmetic schema mappings, that is, schema mappings specified by source-to-target dependencies and target dependencies that may include arithmetic formulas interpreted over the algebraic real numbers (we restrict attention to algebraic real numbers to maintain finite presentability). We show that, for arithmetic schema mappings without target dependencies, the existence-of-solutions problem can be solved in polynomial time, and, if a solution exists, then a universal solution (suitably defined) exists and can be computed in polynomial time. In the case of arithmetic schema mappings with a weakly acyclic set of target dependencies, a universal solution may not exist, but a finite universal basis exists (if a solution exists) and can be computed in polynomial space. The existence-of-solutions problem turns out to be NP-hard, and solvable in PSpace. In fact, we show it is ∃R-complete, which means that it has the same complexity as the decision problem for the existential theory of the real numbers, or, equivalently, the problem of deciding whether or not a quantifier-free arithmetic formula has a solution over the real numbers. If we allow only linear arithmetic formulas in the schema mapping and in the query, interpreted over the rational numbers, then the existence-of-solutions problem is NP-complete. We obtain analogous complexity results for the data complexity of computing the certain answers of arithmetic conjunctive queries and linear arithmetic conjunctive queries.