Representability of Design Objects by Ancestor-Controlled Hierarchical Specifications

Abstract

A simple model, called a VDAG, is proposed for succinctly representing hierarchically specified design data in CAD database systems where there are to be alternate expansions of hierarchical 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 that are VDAG-generable is characterized. It is shown that there are designs whose representation via VDAGs is exponentially more succinct than is possible when expansion is uncontrolled. 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, the paper shows 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.