Constrained Detecting Arrays: Mathematical Structures for Fault Identification in Combinatorial Interaction Testing

TL;DR

This paper introduces Constrained Detecting Arrays (CDAs), extending detecting arrays to systems with constraints, and proposes two algorithms for their construction, validated through experiments on benchmark datasets.

Contribution

The paper develops Constrained Detecting Arrays and provides two algorithms for their efficient construction, addressing the challenge of applying detecting arrays to constrained systems.

Findings

The first algorithm can generate minimum CDAs given enough time.

The second algorithm produces near-minimum CDAs quickly.

Experimental results validate the effectiveness of both algorithms.

Abstract

Context: Detecting arrays are mathematical structures aimed at fault identification in combinatorial interaction testing. However, they cannot be directly applied to systems that have constraints among test parameters. Such constraints are prevalent in real-world systems. Objectives: This paper proposes Constrained Detecting Arrays (CDAs), an extension of detecting arrays, which can be used for systems with constraints. Methods: The paper examines the properties and capabilities of CDAs with rigorous arguments. The paper also proposes two algorithms for constructing CDAs: One is aimed at generating minimum CDAs and the other is a heuristic algorithm aimed at fast generation of CDAs. The algorithms are evaluated through experiments using a benchmark dataset. Results: Experimental results show that the first algorithm can generate minimum CDAs if a sufficiently long generation time is allowed, and the second algorithm can generate minimum or near-minimum CDAs in a reasonable time. Conclusion: CDAs enhance detecting arrays to be applied to systems with constraints. The two proposed algorithms have different advantages with respect to the array size and generation time