Set Of Multivalued Dependencies Research Articles

Characterizing the MVDs That Hold in a Connected Subtree of a Join Tree: A Correction

Given an acyclic database scheme R and a connected subtree T of a join tree for R, this paper provides a characterization of the set of multivalued dependencies (MVDs) that hold over T with respect to infinR, the corresponding join dependency (JD) of R. This result corrects an error in one of my previous papers "A Comparative Study of Various Nested Normal Forms," which was published in vol. 14, no. 2, pp. 369-385, Mar./Apr. 2002.

Unifying functional and multivalued dependencies for relational database design

We consider the problem of unifying functional dependencies (FDs) and multivalued dependencies (MVDs) in designing relational database schemes. Given a set D of dependencies (MVDs and FDs) over a universal scheme U, we define a different set of MVDs over U, called the envelope set for D, so that a database scheme with respect to D can be designed by considering only the MVDs in the envelope set for D, instead of treating MVDs and FDs in D separately. We show that a database scheme is in 4NF with respect to D (BCNF when D has only FDs) if it is 4NF with respect to the envelope set for D. By utilizing the envelope set of dependencies we extend the conflict free property of sets of MVDs to apply to sets of FDs and MVDs. We show that if a set D of dependencies is extended conflict-free, then there exists an acyclic, joint lossless 4NF decomposition (BCNF) with respect to D which is also dependency preserving. Except for the case where D is a set of MVDs only, this was an open problem in the literature. We also show that, for a set M of MVDs, an acyclic join lossless 4NF decomposition exists if M does not split its keys. Given a set of dependencies D, obtaining the envelope set for D, determining whether D is extended conflict free, and if D is extended conflict free, then obtaining a dependency preserving, acyclic, join lossless, 4NF decomposition can be done in time polynomial in the size of D.

Compact scheme forests in nested normal form

In the context of data base design for nested relational structures, update anomalies can be avoided if the nested scheme forest composed of scheme trees is in nested normal form (NNF) with respect to the associated set of data dependencies. In practice, minimizing the number of normal scheme trees in the nested scheme forest, which is in NNF, will also be an important design goal. This is because the number of computationally expensive join operations that are required in order to answer a given query is related to the number of normal scheme trees that must be used in the query expression. We prove that the problem of finding a succinct NNF scheme forest is NP-complete for a subclass of the class of split-free sets of multivalued dependencies.

An Information-Theoretic Analysis of Relational Databases—Part II: Information Structures of Database Schemas

The structural properties of acyclic database schemas, especially the interrelationships between acyclic join dependencies and multivalued dependencies, are examined in this paper. The intersection closure of a database schema is a semilattice, which is usually represented by Hasse diagram in algebra. The Hasse diagram of a schema is analogous to the Bachman diagram of a network model. Based on the topological structures of Hasse diagrams, the acyclic join dependency is proved to be equivalent to a set of conflict-free multivalued dependencies. Furthermore, we show that if the Hasse diagram is loop free, then the corresponding set of multivalued dependencies is also contention-free. This result is consistent with previous results derived from the Bachman diagram.

A new normal form for nested relations

We consider nested relations whose schemes are structured as trees, called scheme trees, and introduce a normal form for such relations, called the nested normal form. Given a set of attributes U , and a set of multivalued dependencies (MVDs) M over these attributes, we present an algorithm to obtain a nested normal form decomposition of U with respect to M . Such a decomposition has several desirable properties, such as explicitly representing a set of full and embedded MVDs implied by M , and being a faithful and nonredundant representation of U . Moreover, if the given set of MVDs is conflict-free, then the nested normal form decomposition is also dependency-preserving. Finally, we show that if M is conflict-free, then the set of root-to-leaf paths of scheme trees in nested normal form decomposition is precisely the unique 4NF decomposition [9, 16] of U with respect to M .

Split-freedom and MVD-intersection: a new characterization of multivalued dependencies having conflict-free covers

Sets of multivalued dependencies (MVDs) having conflict-free covers are important to the theory and design of relational databases [2, 12, 15, 16]. Their desirable properties motivate the problem of testing a set M of MVDs for the existence of a conflict-free cover. In [8] Goodman and Tay have proposed an approach based on the possible equivalence of M to a single (acyclic) join dependency (JD). We remark that their characterization does not lend an insight into the nature of such sets of MVDs. Here, we use notions that are intrinsic to MVDs to develop a new characterization. Our approach proceeds in two stages. In the first stage, we use the notion of “split-free” sets of MVDs and obtain a characterization of sets M of MVDs having split-free covers. In the second, we use the notion of “intersection” of MVDs to arrive at a necessary and sufficient condition for a split-free set of MVDs to be conflict-free. Based on our characterizations, we also give polynomial-time algorithms for testing whether M has split-free and conflict-free covers. The highlight of our approach is the clear insight it provides into the nature of sets of MVDs having conflict-free covers. Less emphasis is given in this paper to the actual efficiency of the algorithms. Finally, as a bonus, we derive a desirable property of split-free sets of MVDs, thereby showing that they are interesting in their own right.