An Algorithm for Dualization in Products of Lattices and Its Applications

  • Authors:
  • Khaled M. Elbassioni

  • Affiliations:
  • -

  • Venue:
  • ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
  • Year:
  • 2002

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Abstract

Let L = L1 脳 ... 脳 Ln be the product of n lattices, each of which has a bounded width. Given a subset A 驴 L, we show that the problem of extending a given partial list of maximal independent elements of A in L can be solved in quasi-polynomial time. This result implies, in particular, that the problem of generating all minimal infrequent elements for a database with semi-lattice attributes, and the problem of generating all maximal boxes that contain at most a specified number of points from a given n-dimensional point set, can both be solved in incremental quasi-polynomial time.