Measuring the structural complexity of feature models

The automated analysis of feature models (FM) is based on SAT, BDD, and CSP - known NP-complete problems. Therefore, the analysis could have an exponential worst-case execution time. However, for many practical relevant analysis cases, state-of-the-art (SOTA) analysis tools quite successfully master the problem of exponential worst-case execution time based on heuristics. So far, however, very little is known about the structure of FMs that cause the cases in which the execution time (hardness) for analyzing a given FM increases unpredictably for SOTA analysis tools. In this paper, we propose to use width measures from graph theory to characterize the structural complexity of FMs as a basis for an estimation of the hardness of analysis operations on FMs with SOTA analysis tools. We present an experiment that we use to analyze the reasonability of graph width measures as metric for the structural complexity of FMs and the hardness of FM analysis. Such a complexity metric can be used as a basis for a unified method to systematically improve SOTA analysis tools.