A study of algorithms relating distributive lattices, median graphs, and Formal Concept Analysis

In this paper, we study structures such as distributive lattices, semilattices, and median graphs from an algorithmic point of view. Such are very useful in classification phylogeny for representing lineage relationships example. A lattice can be considered a graph while ∨-semilattice provided that some conditions holding on triple elements satisfied. Starting structure with different representations, the problem building structures. We make precise propose algorithms checking how graph. Then, adapt to semilattices where bottom element is removed ∨-semilattice. also state terms Formal Concept Analysis representation formal context, i.e., binary table. Moreover, input system implications Duquenne-Guigues basis lattice, compute semilattice. provide examples which illustrate difficulties related these tasks. particular, minimality output lattices condition hard ensure cannot always achieved.