Some combinatorial algorithms connecting hypergraphs

In the relational datamodel the combinatorial algorithms are constructed many authors. The hypergraph is a important concept in the combinatorial theory. The candidate keys play an essential role in the relational datamodel. In this paper, base on hypergraph we present a new combinatorial algorithm that finds all candidate keys of a give relation. Some another results related to the candidate keys are given

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

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

Some problems related to primitive maximal dependencies

This paper gives some results about primitives  maximal dependencies. Some computational problems related to primitive maximal dependencies and antikeys are investigated

On the connections between relations, relation schemes and keys

The relation, relation schemes, keys and antikeys are essential concepts in the relational datamodel. In this paper, we present some computational connections between relations, relation schemes and sets of minimal keys. Some another combinatorial results connecting them also are given

On the computational algorithm related to antikeys

The keys and antikeys play important roles for the investigation of functional dependency in the relational datamodel. The main purpose of this paper is to prove that the time complexity of finding a set of antileys for a given relation scheme S is exponential in the number of attributes. Some another results connecting the functional dependency are given. Key Word and phrase: Relation, relational datamodel, functionsl dependency, relation scheme, generating Armstrong relation, dependency inference, strong schemen, membership problem, closure, closed set, minimal generater, key, minimal key, antikey