Theory of linear and integer programming
Theory of linear and integer programming
Principles of database and knowledge-base systems, Vol. I
Principles of database and knowledge-base systems, Vol. I
Towards a theory of spatial database queries (extended abstract)
PODS '94 Proceedings of the thirteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Variable independence and aggregation closure
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Finitely representable databases
Journal of Computer and System Sciences - Special issue on principles of database systems
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
The DEDALE system for complex spatial queries
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Spatio-temporal data handling with constraints
Proceedings of the 6th ACM international symposium on Advances in geographic information systems
Constraint query languages (preliminary report)
PODS '90 Proceedings of the ninth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Lossless Representation of Topological Spatial Data
SSD '95 Proceedings of the 4th International Symposium on Advances in Spatial Databases
Linear Constraint Query Languages: Expressive Power and Complexity
LCC '94 Selected Papers from the International Workshop on Logical and Computational Complexity
Theory of Relational Databases
Theory of Relational Databases
Variable Independence, Quantifier Elimination, and Constraint Representations
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
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One of the most important advantages of constraint databases is their ability to represent and to manipulate data in arbitrary dimension within a uniform framework. Although the complexity of querying such databases by standard means such as first-order queries has been shown to be tractable for reasonable constraints (e.g. polynomial), it depends badly (roughly speaking exponentially) upon the dimension of the data. A precise analysis of the trade-off between the dimension of the input data and the complexity of the queries reveals that the complexity strongly depends upon the use the input makes of its dimensions. We introduce the concept of orthographic dimension, which, for a convex object O, corresponds to the dimension of the (component) objects O1; ..., On, such that O = O1 × ... × On. We study properties of databases with bounded orthographic dimension in a general setting of o-minimal structures, and provide a syntactic characterization of first-order orthographic dimension preserving queries. The main result of the paper concerns linear constraint databases. We prove that orthographic dimension preserving Boolean combination of conjunctive queries can be evaluated independently of the global dimension, with operators limited to the orthographic dimension, in parallel on the components. This results in an extremely efficient optimization mechanism, very easy to use in practical applications.