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Reasoning About Variability Models Through Network Analysis

Jose Manuel Sanchez, Miguel Angel Olivero, Ruben Heradio, Luis Cambelo, David Fernandez-Amoros

Abstract

Feature models are widely used to capture the configuration space of software systems. Although automated reasoning has been studied for detecting problematic features and supporting configuration tasks, significantly less attention has been given to the systematic study of the structural properties of feature models at scale. The approach fills this gap by examining the models' structure through a network analysis perspective. We focus on three Research Questions concerning (i) the structural patterns exhibited by these graphs, (ii) the extent to which such patterns vary across domains and model sources, and (iii) the usefulness of network-based indicators for understanding, maintaining, and evolving variability models. To answer these questions, we analyze a dataset of 5,709 models from 20 repositories, spanning multiple application domains and varying sizes (ranging from 99 to 35,907 variables on their Boolean translation). To do so, graphs of transitive dependencies and conflicts between features are computed. Our results reveal consistent structural traits (e.g., the predominance of dependency relations, the presence of highly central features, or characteristic node degree distributions) as well as notable domain-specific deviations. These findings ease the identification of maintenance-relevant features, opportunities for modular decomposition, and indicators of structural fragility. This approach provides a scalable, graph-based foundation for the empirical analysis of variability models and contributes quantitative evidence to support future research on their structure and evolution.

Reasoning About Variability Models Through Network Analysis

Abstract

Feature models are widely used to capture the configuration space of software systems. Although automated reasoning has been studied for detecting problematic features and supporting configuration tasks, significantly less attention has been given to the systematic study of the structural properties of feature models at scale. The approach fills this gap by examining the models' structure through a network analysis perspective. We focus on three Research Questions concerning (i) the structural patterns exhibited by these graphs, (ii) the extent to which such patterns vary across domains and model sources, and (iii) the usefulness of network-based indicators for understanding, maintaining, and evolving variability models. To answer these questions, we analyze a dataset of 5,709 models from 20 repositories, spanning multiple application domains and varying sizes (ranging from 99 to 35,907 variables on their Boolean translation). To do so, graphs of transitive dependencies and conflicts between features are computed. Our results reveal consistent structural traits (e.g., the predominance of dependency relations, the presence of highly central features, or characteristic node degree distributions) as well as notable domain-specific deviations. These findings ease the identification of maintenance-relevant features, opportunities for modular decomposition, and indicators of structural fragility. This approach provides a scalable, graph-based foundation for the empirical analysis of variability models and contributes quantitative evidence to support future research on their structure and evolution.
Paper Structure (21 sections, 8 figures, 5 tables, 1 algorithm)

This paper contains 21 sections, 8 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Feature models and automated analysis
  4. Indirect relations and transitive strong graphs
  5. Network analysis for software and FMs
  6. Two motivational examples
  7. A tiny FM that hides some subtle indirect relationships
  8. Structural analysis of a large FM
  9. Computing Strong Graphs
  10. Stage 1: Translating FMs into Boolean formulas
  11. Stage 2: Computing strong relationships
  12. Empirical Network Analysis of FMs
  13. Step 1: Graphs Analysis
  14. Step 2: Core and dead features across domains
  15. Step 3: Dependencies versus conflicts
  16. ...and 6 more sections

Figures (8)

  • Figure 1: An excerpt from the FM of coreboot 4.13.
  • Figure 2: Transitive-closure-based strong graphs for the features in Figure \ref{['lst:kconfig-code']}.
  • Figure 3: Node in-degree distribution in the dependency graph of Linux 2.6.9 X86 64-bit. Most features are required by few others, while a small number act as highly required hubs.
  • Figure 4: In-degree vs. out-degree in the dependency graph of Linux 2.6.9 X86 64-bit. Highly required features tend to have few dependencies, avoiding features that are both highly required and highly dependent.
  • Figure 5: Node degree distribution in the conflict graph of Linux 2.6.9 X86 64-bit. Most features have few conflicts, while a small number of highly constraining features are in conflict with many others.
  • ...and 3 more figures