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Some Complexity Results about Essential Closed Sets

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Formal Concept Analysis (ICFCA 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6628))

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Abstract

We examine the enumeration problem for essential closed sets of a formal context. Essential closed sets are sets that can be written as the closure of a pseudo-intent. The results for enumeration of essential closed sets are similar to existing results for pseudo-intents, albeit some differences exist. For example, while it is possible to compute the lectically first pseudo-intent in polynomial time, we show that it is not possible to compute the lectically first essential closed set in polynomial time unless P = NP. This also proves that essential closed sets cannot be enumerated in the lectic order with polynomial delay unless P = NP. We also look at minimal essential closed sets and show that they cannot be enumerated in output polynomial time unless P = NP.

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References

  1. Babin, M., Kuznetsov, S.: Recognizing pseudo-intents is coNP-complete. In: Kryszkiewicz, M., Obiedkov, S. (eds.) Proc. of the 7th Int. Conf. on Concept Lattices and Their Applications (CLA 2010). CEUR Workshop Proceedings, vol. 672 (2010)

    Google Scholar 

  2. Distel, F.: Hardness of enumerating pseudo-intents in the lectic order. In: Kwuida, L., Sertkaya, B. (eds.) ICFCA 2010. LNCS, vol. 5986, pp. 124–137. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  3. Distel, F., Sertkaya, B.: On the complexity of enumerating pseudo-intents. Discrete Applied Mathematics (2011) (to appear)

    Google Scholar 

  4. Eiter, T., Gottlob, G.: Hypergraph transversal computation and related problems. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 549–564. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Ganter, B.: Two basic algorithms in concept analysis. Preprint 831, Fachbereich Mathematik, TU Darmstadt, Darmstadt, Germany (1984)

    Google Scholar 

  6. Gély, A., Medina, R., Nourine, L., Renaud, Y.: Uncovering and reducing hidden combinatorics in guigues-duquenne bases. In: Ganter, B., Godin, R. (eds.) ICFCA 2005. LNCS (LNAI), vol. 3403, pp. 235–248. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  7. Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives résultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)

    Google Scholar 

  8. Kuznetsov, S.O.: On the intractability of computing the Duquenne-Guigues base. Journal of Universal Computer Science 10(8), 927–933 (2004)

    MathSciNet  MATH  Google Scholar 

  9. Kuznetsov, S.O., Obiedkov, S.: Algorithms for the construction of concept lattices and their diagram graphs. In: Siebes, A., De Raedt, L. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, pp. 289–300. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Kuznetsov, S.O., Obiedkov, S.: Counting Pseudo-intents and #P-completeness. In: Missaoui, R., Schmidt, J. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3874, pp. 306–308. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Obiedkov, S., Duquenne, V.: Attribute-incremental construction of the canonical implication basis. Annals of Mathematics and Artificial Intelligence 49(1-4), 77–99 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  12. Sertkaya, B.: Some computational problems related to pseudo-intents. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 130–145. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Sertkaya, B.: Towards the complexity of recognizing pseudo-intents. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds.) ICCS 2009. LNCS, vol. 5662, pp. 284–292. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Felix Distel

Authors
  1. Felix Distel
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Editors and Affiliations

  1. Département d’Informatique, Université du Québec à Montréal, Succ. Centre-Ville, Montréal, C.P.8888, H3C 3P8, Québec, Canada

    Petko Valtchev

  2. Universität Kassel, Fachgebiet Wissensverarbeitung, Wilhelmshöher Allee 73, 34121, Kassel, Germany

    Robert Jäschke

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Distel, F. (2011). Some Complexity Results about Essential Closed Sets. In: Valtchev, P., Jäschke, R. (eds) Formal Concept Analysis. ICFCA 2011. Lecture Notes in Computer Science(), vol 6628. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20514-9_8

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  • DOI: https://doi.org/10.1007/978-3-642-20514-9_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-20513-2

  • Online ISBN: 978-3-642-20514-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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