Highly configurable software systems are crucial in practice to satisfy the rising demand for software customization, and combinatorial interaction testing (CIT) is an important methodology for testing such systems. Constrained covering array generation (CCAG), as the core problem in CIT, is to construct a$t$-wise covering array (CA) of minimum size, where$t$represents the testing strength. Extensive studies have demonstrated that high-strength CIT (e.g., 4-wise and 5-wise CIT) has stronger fault detection capability than low-strength CIT (i.e., 2-wise and 3-wise CIT), and there exist certain critical faults that can be disclosed through high-strength CIT. Although existing CCAG algorithm has exhibited effectiveness in solving the low-strength CCAG problem, they suffer the severe highstrength challenge when solving 4-wise and 5-wise CCAG, which urgently calls for effective solutions to solving 4-wise and 5 wise CCAG problems. To alleviate the high-strength challenge, we propose a novel and effective local search algorithm dubbed HSCA. Particularly, HSCA incorporates three new and powerful techniques, i.e., multi-round CA generation mechanism, dynamic priority assigning technique, and variable grouping strategy, to improve its performance. Extensive experiments on 35 real-world and synthetic instances demonstrate that HSCA can generate significantly smaller 4-wise and 5-wise CAs than existing state-of-the-art CCAG algorithms. More encouragingly, among all 35 instances, HSCA successfully builds 4-wise and 5-wise CAs for 35 and 29 instances, respectively, including 11 and 15 instances where existing CCAG algorithms fail. Our results indicate that HSCA can effectively mitigate the high-strength challenge.

To meet the rising demand for software customization, highly configurable software systems play key roles in practice. Combinatorial interaction testing (CIT) is recognized as an effective approach for testing such systems. For CIT, the most important problem is constrained covering array generation (CCAG), which aims to construct a minimum-sized t-wise covering array (CA), where t denotes testing strength. Compared to pairwise testing (i.e., 2-wise CIT) that is a widely-used CIT technique, 3-wise CIT can discover more faults and bring more benefit in real-world applications. However, current state-of-the-art CCAG algorithms suffer from the severe scalability challenge for 3-wise CIT, which renders them ineffective in building 3-wise CAs for highly configurable systems. In this work, we perform an empirical study on various practical, highly configurable systems to present that it is promising to build 3-wise CA through extending 2-wise CA. Inspired by this, we propose ScalableCA, a novel and scalable algorithm that can effectively alleviate the scalability challenge for 3-wise CIT. Further, ScalableCA introduces three new and effective techniques, including fast invalidity detection, uncovering-guided sampling, and remainder-aware local search, to enhance its performance. Our experiments on extensive real-world, highly configurable systems show that, compared to current state-of-the-art algorithms, ScalableCA requires one to two orders of magnitude less running time to build 3-wise CA of 38.9% smaller size in average for large-scale instances. Our results indicate that ScalableCA greatly advances the state of the art in 3-wise CIT.