An Algorithm for Partitioning a Set into Simple Parts

The paper describes a method for the structural analysis of abstract data and its applications. A finite set with two numberings, two order relations, and one symmetry relation is considered. An algorithm is proposed for partitioning this set into simple parts determined by compositions of given relations. Each simple part of the set is then partitioned into layers. This model can also be used for analyzing different data admitting similar formalization. It can be used for analyzing structure of some graphs (in particular, graphs describing molecular associations). The proposed algorithms are used for partitioning a complex family into simple ones determined by family relationships and for determining family generations. The algorithms can be applied to analyzing corporations with a family-like structure.