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Zbl 1022.68027
Nourine, Lhouari; Raynaud, Olivier
A fast incremental algorithm for building lattices. (English)
[J] J. Exp. Theor. Artif. Intell. 14, No.2-3, 217-227 (2002). ISSN 0952-813X; ISSN 1362-3079/e

Summary: This paper presents an incremental algorithm to compute the covering graph of the lattice generated by a family ${\cal B}$ of subsets of a totally ordered set $X$. The implementation of this algorithm has $O(((|X|+|{\cal B}|).|{\cal B}|).|{\cal F}|)$ time complexity, where ${\cal F}$ is the number of elements in the lattice. This improves the complexity of the previous algorithms which is roughly in $O(\text{Min}(|X|,|{\cal B}|)^3.|{\cal F}|)$. This algorithm may be used in many applications in computer sciences such as the computations of Galois (concept) lattice, the maximal antichains lattice or the Dedekind-MacNeille completion of a partial order. All these lattices can be computed incrementally using this algorithm without increasing time complexity.

MSC 2000:: *68P05 Data structures
68P15 Database theory
06B99 Lattices

Keywords: incremental algorithm; covering graph

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