  In this paper, a new general decomposition theory inspired from modular graph
decomposition is presented. Our main result shows that, within this general
theory, most of the nice algorithmic tools developed for modular decomposition
are still efficient. This theory not only unifies the usual modular
decomposition generalisations such as modular decomposition of directed graphs
or decomposition of 2-structures, but also star cutsets and bimodular
decomposition. Our general framework provides a decomposition algorithm which
improves the best known algorithms for bimodular decomposition.
