A simple model, called a VDAG, is proposed for representing hierarchically specified design data in CAD database systems where there are to be alternate expansions of hierarchically specified modules. The model uses an ancestor-based expansion scheme to control which instances of submodules are to be placed within each instance of a given module. The approach is aimed at reducing storage space in engineering design database systems, and providing a means for designers to specify alternate expansions of a module.  The expressive power of the VDAG model is investigated, and the set of design forests which are VDAG-generable is characterized. The problem of determining whether a given design forest is VDAG-generable is shown to be  NP -complete, even when the height of the forest is bounded. However, it is shown that determining whether a given forest is VDAG-generable and producing such a VDAG if it exists, can be partitioned into a number of simpler subproblems, each of which may not be too computationally difficult in practice. Furthermore, for forests in a special natural class that has broad applicability, a polynomial time algorithm is provided that determines whether a given forest is VDAG-generable, and produces such a VDAG if it exists. However, we show that it is  NP -hard to produce a minimum-sized such VDAG for forests in this special class, even when the height of the forest is bounded.
['Lin Yu', 'Daniel J. Rosenkrantz']
Representability of design objects by ancestor-controlled hierarchical specifications