Block Decomposition of Inheritance Hierarchies

Inheritance hierarchies play a central role in object oriented languages as in knowledge representation systems. These hierarchies are acyclic directed graphs representing the underline structure of objects. This paper is devoted to the study of eecient algorithms to decompose recursively an inheritance hierarchy into independent subgraphs which are inheritance hierarchies themselves. This process gives a tree called decomposition tree. The decomposition proposed here is based on the concept of block which is an extension of the concept of h-module proposed have presented a linear algorithm to decompose an inheritance hierarchy into h-modules. The algorithm proposed here to decompose an inheritance hierarchy into blocks generalizes the algorithm of Habib et al.. It computes a linear extension of the hierarchy such that the blocks are factors of the extension. This is a general technique applicable to diierent de-compositions 2, 1]. The unicity of the block decomposition comes from a proposition showing the links between blocks and modules of the well known modular decomposition of directed graphs, and from the theorem of unicity of the modular decomposition. While the cost to compute the block decomposition is greater than the h-module decomposition one, it allows a greater factorization of the information of inheritance represented by the hierarchy. This decomposition can be useful for graph drawing applications 6] and could also be used for hierarchy coding applications. Such a decomposition can also be seen as a tool to help object oriented languages programmer to \understand" their hierarchies. Some linearizations of object hierarchies can be deened from this decomposition.