Some problems related to keys and the Boyce-Codd normal form

The aim of this paper is to investigate the connections between minimal keys and antikeys for special Sperner-systems by hypergraphs. The Boyce-Codd normal form and some related problems are also studied in this paper

Determination of the normalization level of database schemas through equivalence classes of attributes

In this paper, based on equivalence classes of attributes there are formulated necessary and sufficient conditions that constraint a database schema to be in the second, third or Boyce-Codd normal forms. These conditions offer a polynomial complexity for the testing algorithms of the normalizations level

Some computational problems related to normal forms

In the relational database theory the most desirable  normal form is the Boyce-Codd normal form (BCNF). This paper investigates some computational problems concerning BCNF relation scheme and BCNF relations. We give an effective algorithm finding a BCNF relation r such that r represents a given BCNF relation scheme s  (i.e., Kr=Ks, where Kr and Ks are  sets of all minimal keys of  r and s). This paper also gives an effective algorithm which  from a given  BCNF relation finds a BCNF relation scheme such that Kr=Ks. Based on these algorithms we prove that  the time  complexity of the  problem that  finds a BCNF relation r  representing a given BCNF relation scheme s is exponential in the size of s and conversely, the complexity of finding a BCNF relation scheme s from a given BCNF relation r such that r represents s also is exponential in the number of attributes. We give a new characterization of the relations and the relation scheme that are uniquely determined by their minimal keys. It is known that these relations and the relation schemes are in the BCNF class. From this characterization we give a polynomial time algorithm deciding whether an arbitrary relation is uniquely determined by its set of all  minimal keys. In the rest if this paper some new bounds of the  size of minimal Armstrong relations for  BCNF relation scheme are given. We show that given a Sperner system K and BCNF relation scheme s a set of minimal keys of which is K, the number of antikeys (maximal nonkeys) of K is polynomial in the number of attributes iff so is the size of minimal Armstrong relation of s

Why is the snowflake schema a good data warehouse design?

Database design for data warehouses is based on the notion of the snowflake schema and its important special case, the star schema. The snowflake schema represents a dimensional model which is composed of a central fact table and a set of constituent dimension tables which can be further broken up into subdimension tables. We formalise the concept of a snowflake schema in terms of an acyclic database schema whose join tree satisfies certain structural properties. We then define a normal form for snowflake schemas which captures its intuitive meaning with respect to a set of functional and inclusion dependencies. We show that snowflake schemas in this normal form are independent as well as separable when the relation schemas are pairwise incomparable. This implies that relations in the data warehouse can be updated independently of each other as long as referential integrity is maintained. In addition, we show that a data warehouse in snowflake normal form can be queried by joining the relation over the fact table with the relations over its dimension and subdimension tables. We also examine an information-theoretic interpretation of the snowflake schema and show that the redundancy of the primary key of the fact table is zero

Integration of multi lifecycle assessment and design for environment database using relational moddel concepts

Multi-lifecycle Assessment (MLCA) systematically considers and quantifies the consumption of resources and the environmental impact associated with a product or process. Design challenges posed by a multi-lifecycle strategy are significantly more complex than traditional product design. The designer must look forward in time to maximize the product\u27s end-of-life yield of assemblies, parts and materials while looking backward to the world of existing products for feedstock sources for the current design. As MLCA and DEE share some common data items, such as, part geometry, material and manufacturing process, it is advantageous to integrate the database for MLCA and DEE. The integration of CAD/DEE and MLCA database will provide not only to designers but also for dernanufacturer and MLCA analyst to play an active role in achieving the vision of sustainability. The user of MLCA software has to provide a significant amount of information manually about a product for which the environmental burdens are being analyzed, which is an error prone activity. To avoid the manual work and associative problems, a MLCA-CAD interface has been developed to progranmtatically populate the MLCA database by using the Bill of Material (BOM) information in the CAD software. This MLCA-CAD interface provides a flow of information from design software (DEE/CAD) to MLCA software

Direct Product Decompositions of Lattices, Closures and Relation Schemes

In this paper we study direct product decompositions of closure operations and lattices of closed sets. We characterize direct product decompositions of lattices of closed sets in terms of closure operations, and find those decompositions of lattices which correspond to the decompositions of closures. If a closure on a finite set is represented by its implication base (i.e. a binary relation on a powerset), we construct a polynomial algorithm to find its direct product decompositions. The main characterization theorem is also applied to define direct product decompositions of relational database schemes and to find out what properties of relational databases and schemes are preserved under decompositions