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<p>A paradigm is proposed for representing hierarchically specified design data in CAD database systems in which there are alternate expansions of hierarchically specified modules. The paradigm uses an ancestor-based scheme to control which instances of submodules are to be placed in the expansion of each instance of a given module and is formalized using a versioned directed acyclic multigraph (VDAG). The approach is aimed at reducing storage space in engineering design database systems and at providing a means for designers to specify alternate expansions of a module. The VDAG model is defined, and a mechanism by which a VDAG generates an exploded forest of design trees is described. Algorithms are provided to generate a design forest from a given VDAG, determine whether one module is contained by a larger module, extract a version from a VDAG, test whether two VDAGs are equivalent, and try to reduce the size of a VDAG. The problems of module containment and VDAG inequivalence are shown to be NP-complete, and the problem of finding a minimum sized VDAG equivalent to a given VDAG is shown to be NP-hard.</p>
hierarchically specified design data; CAD database systems; hierarchically specified modules; ancestor-based scheme; versioned directed acyclic multigraph; VDAG; engineering design database systems; exploded forest; design trees; VDAG inequivalence; NP-complete; minimum sized VDAG; CAD; database management systems; graph theory

L. Yu and D. Rosenkrantz, "Ancestor Controlled Submodule Inclusion in Design Databases," in IEEE Transactions on Knowledge & Data Engineering, vol. 5, no. , pp. 352-362, 1993.
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