On Verifying and Engineering the Well-gradedness of a Union-closed Family

  title={On Verifying and Engineering the Well-gradedness of a Union-closed Family},
  author={D. Eppstein and J. Falmagne and Hasan Uzun},
  • D. Eppstein, J. Falmagne, Hasan Uzun
  • Published 2007
  • Mathematics, Computer Science
  • ArXiv
  • Abstract Current techniques for generating a knowledge space, such as QUERY, guarantee that the resulting structure is closed under union, but not that it satisfies wellgradedness, which is one of the defining conditions for a learning space. We give necessary and sufficient conditions on the base of a union-closed set family that ensures that the family is well-graded. We consider two cases, depending on whether or not the family contains the empty set. We also provide algorithms for… CONTINUE READING

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