Bit-vector encoding for partially ordered sets

  • Michel Habib
  • Lhouari Nourine
Invited Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 831)


Given a lattice L, we propose a tree representation of L. We show that this tree contains a bit-vector encoding of L and then how to compute from this tree the lattice operations (meet and join). Algorithms which provide bit-vectors encodings for partial orders have been recently proposed in the literature. Given a partial order P we recall that computing an optimal bit-vector encoding of P is NP-Complete. From a theoretical lattice point of view we propose bit-vector encodings and study their optimality. We end by suggesting a data structure (lazy MacNeille completion) which can have many applications.


Lattice theory Galois lattice MacNeille Completion Distributive Lattice and Lattice of Ideals Bit Vector Encoding Bounded Dimension 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Michel Habib
    • 1
  • Lhouari Nourine
    • 1
  1. 1.Département d'Informatique Fondamentale LIRMMUniversité Montpellier IIMontpellier Cedex 5France

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