The poset of closures as a model of changing databases

Burosch, Gustav; Demetrovics, János; Katona, Gyula O. H.

doi:10.1007/bf00337692

Cited by 33 publications

(8 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The second kind of problem in our study is the complexity of hypergraph saturation, a covering problem for the powerset P(S) of a finite set S considered in [51,10]. We introduce some notation first.…”

Section: Examplementioning

confidence: 99%

Identifying the Minimal Transversals of a Hypergraph and Related Problems

1995

View full text Add to dashboard Cite

The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation, i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H, is shown to be co-NP-complete. A certain subproblem of hypergraph saturation, the saturation of simple hypergraphs (i.e. Sperner families), is shown to be under polynomial transformation equivalent to transversal hypergraph recognition, i.e., given two hypergraphs H 1 ; H 2 , decide if the sets in H 2 are all the minimal transversals of H 1. The complexity of the search problem related to the recognition of the transversal hypergraph, the computation of the transversal hypergraph, is an open problem. This task needs time exponential in the input size; it is unknown whether an output-polynomial algorithm exists. For several important subcases, for instance if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs, output-polynomial algorithms are presented. Computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice, which is pointed out by identifying important applications in database theory, Boolean switching theory, logic, and AI, particularly in model-based diagnosis.

show abstract

Section: Examplementioning

confidence: 99%

Identifying the Minimal Transversals of a Hypergraph and Related Problems

1995

View full text Add to dashboard Cite

show abstract

“…It is easy to see that there is a t such that {a}~~X(1)~...~X Ct ) = XCt+I) = ... and we set {a}+ = xCt). (1)!i E8 or Ii = {a}~{a}, (2) Ii is the rusult of applying the 82 to two of 8Ds h, ..., Ii-I, (3) Ii is the rusult of applying the 83 to one of 8Ds h,···, Ii-I, (4) Ii is the rusult of applying the 84 or 85 to two of 8Ds h, ... , Ii-I, Ii+l is the result of applying 55 (54) two 5Ds Ip = {a} ---t C and Iq = {a} ---t D (p, q~i) then by the induction hypothesis there are X(l} and X(h) such that C~X(I), D~X(h). We set s = max(l, h), then B = CuD~X(s) and B = enD~x(l}.…”

Section: Algorithm 1 (Finding {A}+)mentioning

confidence: 99%

Armstrong relations and strong dependencies

Thi¹

2016

JCC

View full text Add to dashboard Cite

Abstract. In this paper, the concept of strong scheme is introduced.We prove that the membership problem for strong dependencies ill solved by an algorithm in polynomial time.We give a necessary and sufficient condition for a relation to be Armstrong relation of a given strong scheme.Keyword and Phrases: Relation, relation datamodel, strong scheme, membership problem, SD-relation implication problem.Bff-relation equivalence problem, closure, closed set. RESULTSDefinition 1. Let U be a nonempty finite set, R = {hI, ..., hm} relation over U and A, U~U. We say that B strongly depend on A in R (denote A ; I B) if Definition 3. Let U = {aI, ..., an} be a nonempty finite set attributes and P(U) its power set. Let Y~P(U) X P(U). We say Y is a s-family if all A, B, C, D~U and a E U

show abstract

“…By a polynomial time algorithm finding a set of all antikeys of a given relation (see [14]) and according to Theorem 7 we obtain the followwing proposition. The size of minimal Armstrong relation was investigated in some papers (see [2,5,6,12,14]). Now we present some new bounds for the size of Armstrong relation.…”

Section: Algorithmmentioning

confidence: 99%

An ninh dữ liệu và an ninh các mạng LAN

Nam¹

2016

JCC

View full text Add to dashboard Cite

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., K; = Ks, where K; and Ks are sets of all minimal keys of T and s). This paper also gives an effective algorithm which from a given BCNF relation finds a BCNF relation scheme such that K; = K8• Based on these algorithms we prove that the time complexity of the problem that finds a BCNF relation T 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 T such that T represents s also is exponential in the number of attributes. We give a new characterization of the relations and the relation schemes 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 of 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, tl.l.enumber of antikeys (maximal nonkeys) of K is polynomial in the number of attributes iff so is the size of minimal Armstrong relation of s.

show abstract

The poset of closures as a model of changing databases

Cited by 33 publications

References 3 publications

Identifying the Minimal Transversals of a Hypergraph and Related Problems

Identifying the Minimal Transversals of a Hypergraph and Related Problems

Armstrong relations and strong dependencies

An ninh dữ liệu và an ninh các mạng LAN

Contact Info

Product

Resources

About