autodb (version 2.3.1)

synthesise: Synthesise relation schemas from functional dependencies

Description

Synthesises the dependency relationships in dependencies into a database schema satisfying at least third normal form, using Bernstein's synthesis.

Usage

synthesise(
  dependencies,
  ensure_lossless = TRUE,
  reduce_attributes = TRUE,
  remove_avoidable = FALSE,
  constants_name = "constants",
  progress = FALSE,
  progress_file = ""
)

Value

A relation_schema object, containing the synthesised relation schemas.

Arguments

dependencies

a functional_dependency object, as given by discover.

ensure_lossless

a logical, TRUE by default. If TRUE, and the decomposition isn't lossless, an extra relation is added to make the decomposition lossless.

reduce_attributes

a logical, TRUE by default. If TRUE, dependencies are checked for determinant attributes that are made redundant by the other dependencies. This is redundant if dependencies is output from discover, since there will be no such redundant attributes.

remove_avoidable

a logical, indicating whether to remove avoidable attributes in relations. If so, then an attribute are removed from relations if the keys can be changed such that it is not needed to preserve the given functional dependencies.

constants_name

a scalar character, giving the name for any relation created to store constant attributes. If this is the same as a generated relation name, it will be changed, with a warning, to ensure that all relations have a unique name.

progress

a logical, for whether to display progress to the user during dependency search in discover.

progress_file

a scalar character or a connection. If progress is non-zero, determines where the progress is written to, in the same way as the file argument for cat.

Details

Bernstein's synthesis is a synthesis algorithm for normalisation of a set of dependencies into a set of relations that are in third normal form. This implementation is based on the version given in the referenced paper.

The implementation also includes a common additional step, to ensure that the resulting decomposition is lossless, i.e. a relation satisfying the given dependencies can be perfectly reconstructed from the relations given by the decomposition. This is done by adding an additional relation, containing a key for all the original attributes, if one is not already present.

As an additional optional step, schemas are checked for "avoidable" attributes, that can be removed without loss of information.

Constant attributes, i.e. those whose only determinant set is empty, get assigned to a relation with no keys.

Output is independent of the order of the input dependencies: schemas are sorted according to their simplest keys.

Schemas are sorted before ensuring for losslessness, or removing avoidable attributes. As a result, neither optional step changes the order of the schemas, and ensuring losslessness can only add an extra schema to the end of the output vector.

References

3NF synthesis algorithm: Bernstein P. A. (1976) Synthesizing third normal form relations from functional dependencies. ACM Trans. Database Syst., 1, 4, 277--298.

Removal of avoidable attributes: Ling T., Tompa F. W., Kameda T. (1981) An improved third normal form for relational databases. ACM Trans. Database Syst., 6, 2, 329--346.

Examples

# example 6.24 from The Theory of Relational Databases by David Maier
# A <-> B, AC -> D, AC -> E, BD -> C
deps <- functional_dependency(
  list(
    list("A", "B"),
    list("B", "A"),
    list(c("A", "C"), "D"),
    list(c("A", "C"), "E"),
    list(c("B", "D"), "C")
  ),
  attrs_order = c("A", "B", "C", "D", "E")
)
synthesise(deps, remove_avoidable = FALSE)
synthesise(deps, remove_avoidable = TRUE)