A Generic Algorithm for Generating Closed Sets of a Binary Relation

  • Alain Gély
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3403)


In this paper we propose a “divide and conquer” based generating algorithm for closed sets of a binary relation. We show that some existing algorithms are particular instances of our algorithm. This allows us to compare those algorithms and exhibit that the practical efficiency relies on the number of invalid closed sets generated. This number strongly depends on a choice function and the structure of the lattice. We exhibit a class of lattices for which no invalid closed sets are generated and thus reduce time complexity for such lattices. We made several tests which illustrate the impact of the choice function in practical efficiency.


Generation algorithm Closure operator Galois or concept lattice 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Alain Gély
    • 1
  1. 1.LIMOSUniversité Blaise PascalAubière CedexFrance

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