Generation Algorithm of a Concept Lattice with Limited Object Access

Classical algorithms for generating the concept lattice (C, ) of a binary table (O,I,R) have a complexity in O(|C| | I| 2 | O|). Although the number of concepts is exponential in the size of the table in the worst case, the generation of a concept is output polynomial. In practice, the number of concepts is often polynomial in the size of the table. However, the cost of generating a concept remains high when the table is composed of a large number of objects. We propose in this paper an algorithm for generating the lattice with limited object access, which can improve the computation time. Experi- ments were conducted with Joomla!, a content management system based on relational algebra, and located on a MySQL database.