Complexity Tailored Design: A New Design Methodology for Databases With Incomplete Information

Abstract

This paper introduces a new design methodology, Complexity Tailored Design, for databases containing incomplete information. The novelty of the approach is that it introduces query complexity as a consideration in database design. In general, the problem of evaluating queries in databases with incomplete information is intractable. Complexity Tailored Design consists in setting the values of database design parameters so as to guarantee the e cient (polynomial time) evaluability of selected queries. We develop this approach for OR-databases, which are obtained by extending relational databases with OR-objects that express restricted disjunctions; OR-objects occur naturally in planning, scheduling and design applications. We consider two design parameters: (i) typing that delimits the columns in which OR-objects may occur, and (ii) degree of coreference that determines how OR-objects may be repeated within the database. We establish, for a broad class of queries in OR-databases, a complete syntactic characterization that classi es the data complexity of each query as being either in PTIME or co-NP complete, given a setting of the database design parameters. This characterization can then be used in complexity tailored design to determine \maximal" schemata for which the queries of interest to the user are evaluable in PTIME.

On the Computational Complexity of Minimal-Change Integrity Maintenance in Relational Databases

“…It is shown how the complexity depends on whether the tables satisfy various schema-level criteria, governing the allowed occurrences of OR-objects. Since there is no exact correspondence between tables with OR-objects and sets of repairs of a given database instance, the results of the paper [54] do not directly translate to our framework, and vice versa. A different interesting direction to explore in this context is to consider conditional tables, proposed by Imieliński and Lipski [52], as a representation for infinite sets of repairs, as in Example 8.…”

“…The need to accommodate violations of functional dependencies is one of the main motivations for considering disjunctive databases (studied, among others, by Imieliński, van der Meyden, Naqvi, and Vadaparty [53,54,61] and has led to various proposals in the context of data integration (Agarwal et al [3], Baral et al [10], Dung [32], and Lin and Mendelzon [58]). There seems to be an intriguing connection between relation repairs w.r.t.…”

“…Known tractable classes of first-order queries over disjunctive databases typically involve conjunctive queries and databases with restricted OR-objects [53,54]. In some cases, like in Example 3, the set of all repairs can be represented as a table with OR-objects.…”

“…But in general a correspondence between sets of repairs and tables with OR-objects holds only in the very restricted case when the relation is binary, say R(A, B), and there is one FD A → B [8]. Imieliński, van der Meyden, and Vadaparty [54] provide a complete classification of the complexity of conjunctive queries for tables with OR-objects. It is shown how the complexity depends on whether the tables satisfy various schema-level criteria, governing the allowed occurrences of OR-objects.…”

Query Answering in Inconsistent Databases

“…This approach is limited to primary key functional dependencies and was subsequently generalized to other key functional dependencies by Dung [37]. In the same context, Baral et al [13,53] proposed to use disjunctive Datalog, and Lin and Mendelzon [79] tables with OR-objects [62,63]. Agarwal et al [2] introduced flexible relational algebra to query flexible relations, and Dung [37] introduced flexible relational calculus (a proper subset of the calculus can be translated to flexible relational algebra).…”