Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Constructing Armstrong tables for general cardinality constraints and not-null constraints

Constructing Armstrong tables for general cardinality constraints and not-null constraints Integrity constraints capture relevant requirements of an application that should be satisfied by every state of the database. The theory of integrity constraints is largely a theory over relations. To make data processing more efficient, SQL permits database states to be partial bags that can accommodate incomplete and duplicate information. Integrity constraints, however, interact differently on partial bags than on the idealized special case of relations. In this current paper, we study the implication problem of the combined class of general cardinality constraints and not-null constraints on partial bags. We investigate structural properties of Armstrong tables for general cardinality constraints and not-null constraints, and prove exact conditions for their existence. For the fragment of general max-cardinality constraints, unary min-cardinality constraints and not-null constraints we show that the effort for constructing Armstrong tables is precisely exponential. For the same fragment we provide an axiomatic characterization of the implication problem. The major tool for establishing our results is the Hajnal and Szemerédi theorem on the equitable colorings of graphs. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annals of Mathematics and Artificial Intelligence Springer Journals

Constructing Armstrong tables for general cardinality constraints and not-null constraints

Loading next page...
 
/lp/springer-journals/constructing-armstrong-tables-for-general-cardinality-constraints-and-gyiytPm45Y

References (25)

Publisher
Springer Journals
Copyright
Copyright © 2014 by Springer International Publishing Switzerland
Subject
Computer Science; Artificial Intelligence (incl. Robotics); Mathematics, general; Computer Science, general; Statistical Physics, Dynamical Systems and Complexity
ISSN
1012-2443
eISSN
1573-7470
DOI
10.1007/s10472-014-9423-9
Publisher site
See Article on Publisher Site

Abstract

Integrity constraints capture relevant requirements of an application that should be satisfied by every state of the database. The theory of integrity constraints is largely a theory over relations. To make data processing more efficient, SQL permits database states to be partial bags that can accommodate incomplete and duplicate information. Integrity constraints, however, interact differently on partial bags than on the idealized special case of relations. In this current paper, we study the implication problem of the combined class of general cardinality constraints and not-null constraints on partial bags. We investigate structural properties of Armstrong tables for general cardinality constraints and not-null constraints, and prove exact conditions for their existence. For the fragment of general max-cardinality constraints, unary min-cardinality constraints and not-null constraints we show that the effort for constructing Armstrong tables is precisely exponential. For the same fragment we provide an axiomatic characterization of the implication problem. The major tool for establishing our results is the Hajnal and Szemerédi theorem on the equitable colorings of graphs.

Journal

Annals of Mathematics and Artificial IntelligenceSpringer Journals

Published: Jun 25, 2014

There are no references for this article.