Improving the Performance of Lindig-Style Algorithms with Empty Intersections

The building of a concept lattice and its line diagram from a set of formal concepts is an important task in formal concept analysis (FCA), since it allows one to express relationships among formal concepts in a concise and comprehensible form. One may enumerate direct neighbors of each formal concept and build a concept lattice or its line diagram in a straightforward way. This is the main idea behind the algorithm proposed by Lindig. This algorithm, as well as other algorithms in FCA, must contend with the fact that some formal concepts are enumerated multiple times. In practice a substantial amount of redundant computations is related to the top (or bottom) formal concept. The In-Close4 algorithm came up with an optimization technique that allows one to eliminate such redundant computations and significantly improves the performance of algorithms from the Close-by-One family. We show that this technique can be used in the Lindig-type algorithms to improve their performance as well.