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The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
In database design, a lossless join decomposition is a decomposition of a relation into relations , such that a natural join of the two smaller relations yields back the original relation. This is central in removing redundancy safely from databases while preserving the original data. [ 1 ]
A decomposition of R into (X, Y) and (X, R − Y) is a lossless-join decomposition if and only if X Y holds in R. Every FD ( functional dependency ) is an MVD (multivalued dependency) because if X → {\displaystyle \rightarrow } Y, then swapping Y's between tuples that agree on X doesn't create new tuples.
Object-oriented decomposition breaks a large system down into progressively smaller classes or objects that are responsible for part of the problem domain. According to Booch, algorithmic decomposition is a necessary part of object-oriented analysis and design, but object-oriented systems start with and emphasize decomposition into objects. [2]
Intuitively, if a functional dependency X → Y holds in R, then the relation can be safely split in two relations alongside the column X (which is a key for () ()) ensuring that when the two parts are joined back no data is lost, i.e. a functional dependency provides a simple way to construct a lossless join decomposition of R in two smaller ...
Object–relational impedance mismatch is a set of difficulties going between data in relational data stores and data in domain-driven object models. Relational Database Management Systems (RDBMS) is the standard method for storing data in a dedicated database, while object-oriented (OO) programming is the default method for business-centric design in programming languages.
Database normalization is the process of structuring a relational database accordance with a series of so-called normal forms in order to reduce data redundancy and improve data integrity.
The chase is a simple fixed-point algorithm testing and enforcing implication of data dependencies in database systems.It plays important roles in database theory as well as in practice.