On the complexity of join dependencies

Marc Gyssens
1986 ACM Transactions on Database Systems  
In [IO] a method is proposed for decomposing join dependencies (jds) in a relational database using the notion of a hinge. This method was subsequently studied in [ll] and [El. We show how the technique of decompasiti"" can be used t" make integrity checking m"re efficient. It turns ""t that it is important t" find a decomposition that minimizes the "umber of edges of its largest element. We show that the decompositions obtained with the method described in (lo] are optimal in this respect.
more » ... minimality criterion leads ta the definition of the degree of cy&ity, which allows us t" classify jds and leads to the notion of n-cyel*i@, of which acyclicity is a special case for n = 2. We then show that, for a fixed value of n (which may be greater than 2). integrity checking can be performed in polynomial time provided we restrict ourselves t" n-cyclic jds. Finally, we generalize a well-known characterization for acyclic jds by proving that n-cyclicity is equivalent ta "n-wise consistency implies global consistency." As a consequence, consistency checking can be performed in polynomial time if we restrict aurselves to n-cyclic jds, for a tired value of n, not necessarily equal t" 2.
doi:10.1145/5236.5237 fatcat:6kociyzrpjhuziagi4baselj4y