AN ALGORITHM FOR ASSESSING DESIGN COMPLEXITY THROUGH A CONNECTIVITY VIEW

ABSTRACT This paper describes an algorithm that is developed to quantify the connectivity of a graph. This connectivity is one of three aspects of complexity (connectivity, solvability, size) that has been identified in previous research. The complexity measures are applied against three components of design: the design problem, the design process, and the design artifact. This algorithm is illustrated step by step through an example. KEYWORDS design complexity, graph connectivity, coupling 1. INTRODUCTION Researchers in design have identified complexity as an important aspect of investigation. One of the common views of complexity that has been identified is the aspect of interconnectivity or the coupling between elements (1). Many of the approaches proposed in the literature have suggested that the coupling is a general measure of the depth of a tree or the number of relations between elements. Here, we propose a connectivity algorithm that may be used in both tree and graph formats. This connectivity algorithm is based upon minimal graph breaking. Coupling as a measure of complexity in design may be developed for the design problem, design artifact, and design process as an extension of the concept provided by (2). This coupling looks at the connections between variables or entities at multiple levels. This coupling measure requires that the representation of that which is being measures be in a graph-based format. Design processes may be represented in graph form where the tasks are nodes of a graph and they are connected through variable dependency (3). Bashir and Thompson’s coupling measure is limited to trees (2). An extension for measuring the coupling of any type of graph is suggested here. It should be noted that this is not the only approach to measuring the coupling of graphs. The graph decomposition is a measure of how decomposable the graph may be. Removing relationships until the graph is separated into sub-graphs demonstrates the coupling found in an entity-relation graph. This algorithm may be recursively applied to the divided graphs to continue the analysis. The algorithm attempts to break the graph into separate sub-graphs, which in turn are broken into sub-graphs. In order to illustrate the algorithm, two examples are provided. These examples are actually derived from two different graph based representations of design exemplars developed to retrieve boss protrusions from solid models (4). The specific details of the entities and relations are stripped from the models to focus exclusively on the connectivity algorithm. It should be noted that we argue in (1) that complexity should not be viewed singularly, but as a composite that includes size (amount of information represented), solvability (difficulty in evaluation/degree of freedom), and coupling (connectivity). Following the algorithm discussion and the provided examples, a brief analysis of the complexity of the algorithm is provided. It is argued that any measure of complexity is valuable only if it is readily calculated (5; 6). Finally, a brief outlook to future applications of this approach is provided in concluding remarks.