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Some combinatorial characteristics of closure operations. (English) Zbl 1445.68080

Summary: The aim of this paper investigates some combinatorial characteristics of minimal key and antikey of closure operations. We also give effective algorithms finding minimal keys and antikeys of closure operations. We estimate these algorithms. Some remarks on the closeness of closure operations class under the union and direct product operations are also studied in this paper.

MSC:

68P15 Database theory
06A15 Galois correspondences, closure operators (in relation to ordered sets)
68R05 Combinatorics in computer science
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References:

[1] W. W. Armstrong, Dependency structures of database relationships, Information processing, 74 (1974) 580-583.
[2] N. Caspard, B. Monjardet, The lattices of closure systems, closure operators, and implicational systems on a finite set: a survey, Discrete Applied Mathematics 127 · Zbl 1026.06008
[3] J. Demetrovics, Z. Furedi, G.O.H. Katona, Minimum matrix representation of closure operations, Discrete Applied Mathematics 11 (1985) 115-128. · Zbl 0577.68084
[4] J. Demetrovics, G. Hencsey, L. Libkin, I. Muchnik, On the interaction between closure operations and choice functions with applications to relational databases, · Zbl 0787.68032
[5] Hirohisa S., Yuga H., Shinya N., On Enumerating Frequent Closed Patterns with Key in Multi-relational Data, Discovery Science: 13th International Conference, DS
[6] C. Lucchese, S. Orlando, R. Perego. Mining frequent closed itemsets out of core. Proceedings of the Sixth SIAM International Conference on Data Mining, (2006)
[7] H. Mao, S. Liu, Posets and closure operators relative to matroids, Matematika, (2012) 77-85.
[8] Vu Duc Nghia, Bina Ramamurthy, Properties of composite of closure operations and choice functions, Acta Cybernetica 15 (2002) 457-465. · Zbl 1064.68038
[9] Vu Duc Nghia,
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