Class Of Functional Dependencies Research Articles

Database Repairing with Soft Functional Dependencies

A common interpretation of soft constraints penalizes the database for every violation of every constraint, where the penalty is the cost (weight) of the constraint. A computational challenge is that of finding an optimal subset: a collection of database tuples that minimizes the total penalty when each tuple has a cost of being excluded. When the constraints are strict (i.e., have an infinite cost), this subset is a “cardinality repair” of an inconsistent database; in soft interpretations, this subset corresponds to a “most probable world” of a probabilistic database, a “most likely intention” of a probabilistic unclean database, and so on. Within the class of functional dependencies, the complexity of finding a cardinality repair is thoroughly understood. Yet, very little is known about the complexity of finding an optimal subset for the more general soft semantics. The work described in this manuscript makes significant progress in that direction. In addition to general insights about the hardness and approximability of the problem, we present algorithms for two special cases (and some generalizations thereof): a single functional dependency, and a bipartite matching. The latter is the problem of finding an optimal “almost matching” of a bipartite graph where a penalty is paid for every lost edge and every violation of monogamy. For these special cases, we also investigate the complexity of additional computational tasks that arise when the soft constraints are used as a means to represent a probabilistic database in the case of a probabilistic unclean database.

SQL schema design: foundations, normal forms, and normalization

Normalization helps us find a database schema at design time that can process the most frequent updates efficiently at run time. Unfortunately, relational normalization only works for idealized database instances in which duplicates and null markers are not present. On one hand, these features occur frequently in real-world data compliant with the industry standard SQL, and especially in modern application domains. On the other hand, the features impose challenges that make it difficult to extend the existing forty year old normalization framework to SQL, and any current extensions are fairly limited.We introduce a new class of functional dependencies and show that they provide the right notion for SQL schema design. Axiomatic and linear-time algorithmic characterizations of the associated implication problem are established. These foundations enable us to propose a Boyce–Codd normal form for SQL. We justify the normal form by showing that it permits precisely those SQL instances which are free from data redundancy. Unlike the relational case, there are SQL schemata that cannot be converted into Boyce–Codd normal form. Nevertheless, for an expressive sub-class of our functional dependencies we establish a normalization algorithm that always produces a schema in Value-Redundancy free normal form. This normal form permits precisely those instances which are free from any redundant data value occurrences other than the null marker. Experiments show that our functional dependencies occur frequently in real-world data and that they are effective in eliminating redundant values from these data sets without loss of information.

Empirical evidence for the usefulness of Armstrong relations in the acquisition of meaningful functional dependencies

Armstrong relations satisfy precisely those data dependencies that are implied by a given set of data dependencies. A common perception is that Armstrong relations are useful in the acquisition of data semantics, in particular since errors during the requirements elicitation have the most expensive consequences. We report on some first empirical evidence for this perception regarding the class of functional dependencies (FDs). For this purpose, we investigate the usefulness of Armstrong relations with respect to various measures. Soundness measures how many of the as meaningful perceived FDs are actually meaningful. Completeness measures how many of the actually meaningful FDs are also perceived as meaningful. Our experiment determines what and how much design teams learn about the application domain in addition to what they know prior to using Armstrong relations. The data analysis suggests that in using Armstrong relations it is not more likely to recognize meaningless FDs which are incorrectly perceived as meaningful, but it is more likely to recognize meaningful FDs that are incorrectly perceived as meaningless. Our measures assess the quality of an FD set with respect to a target FD set, and therefore qualify naturally for the use in automated assessment tools, e.g. for database course exams or assignments.