Abstract
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.
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Habib, M., Nourine, L. (1994). Bit-vector encoding for partially ordered sets. In: Bouchitté, V., Morvan, M. (eds) Orders, Algorithms, and Applications. ORDAL 1994. Lecture Notes in Computer Science, vol 831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0019423
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DOI: https://doi.org/10.1007/BFb0019423
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