A Survey of Constrained Combinatorial Testing

Combinatorial Testing (CT) is a potentially powerful testing technique, whereas its failure revealing ability might be dramatically reduced if it fails to handle constraints in an adequate and efficient manner. To ensure the wider applicability of CT in the presence of constrained problem domains, large and diverse efforts have been invested towards the techniques and applications of constrained combinatorial testing. In this paper, we provide a comprehensive survey of representations, influences, and techniques that pertain to constraints in CT, covering 129 papers published between 1987 and 2018. This survey not only categorises the various constraint handling techniques, but also reviews comparatively less well-studied, yet potentially important, constraint identification and maintenance techniques. Since real-world programs are usually constrained, this survey can be of interest to researchers and practitioners who are looking to use and study constrained combinatorial testing techniques

Deleting and Testing Forbidden Patterns in Multi-Dimensional Arrays

Understanding the local behaviour of structured multi-dimensional data is a fundamental problem in various areas of computer science. As the amount of data is often huge, it is desirable to obtain sublinear time algorithms, and specifically property testers, to understand local properties of the data. We focus on the natural local problem of testing pattern freeness: given a large $d$-dimensional array $A$ and a fixed $d$-dimensional pattern $P$ over a finite alphabet, we say that $A$ is $P$-free if it does not contain a copy of the forbidden pattern $P$ as a consecutive subarray. The distance of $A$ to $P$-freeness is the fraction of entries of $A$ that need to be modified to make it $P$-free. For any $\epsilon \in [0,1]$ and any large enough pattern $P$ over any alphabet, other than a very small set of exceptional patterns, we design a tolerant tester that distinguishes between the case that the distance is at least $\epsilon$ and the case that it is at most $a_d \epsilon$, with query complexity and running time $c_d \epsilon^{-1}$, where $a_d < 1$ and $c_d$ depend only on $d$. To analyze the testers we establish several combinatorial results, including the following $d$-dimensional modification lemma, which might be of independent interest: for any large enough pattern $P$ over any alphabet (excluding a small set of exceptional patterns for the binary case), and any array $A$ containing a copy of $P$, one can delete this copy by modifying one of its locations without creating new $P$-copies in $A$. Our results address an open question of Fischer and Newman, who asked whether there exist efficient testers for properties related to tight substructures in multi-dimensional structured data. They serve as a first step towards a general understanding of local properties of multi-dimensional arrays, as any such property can be characterized by a fixed family of forbidden patterns

Efficient algorithms for reconfiguration in VLSI/WSI arrays

The issue of developing efficient algorithms for reconfiguring processor arrays in the presence of faulty processors and fixed hardware resources is discussed. The models discussed consist of a set of identical processors embedded in a flexible interconnection structure that is configured in the form of a rectangular grid. An array grid model based on single-track switches is considered. An efficient polynomial time algorithm is proposed for determining feasible reconfigurations for an array with a given distribution of faulty processors. In the process, it is shown that the set of conditions in the reconfigurability theorem is not necessary. A polynomial time algorithm is developed for finding feasible reconfigurations in an augmented single-track model and in array grid models with multiple-track switche

Extremal sets with forbidden configurations and the independence ratio of geometric hypergraphs

No abstrac

Comparative Analysis of Constraint Handling Techniques for Constrained Combinatorial Testing

Constraints depict the dependency relationships between parameters in a software system under test. Because almost all systems are constrained in some way, techniques that adequately cater for constraints have become a crucial factor for adoption, deployment and exploitation of Combinatorial Testing (CT). Currently, despite a variety of different constraint handling techniques available, the relationship between these techniques and the generation algorithms that use them remains unknown, yielding an important gap and pressing concern in the literature of constrained combination testing. In this paper, we present a comparative empirical study to investigate the impact of four common constraint handling techniques on the performance of six representative (greedy and search-based) test suite generation algorithms. The results reveal that the Verify technique implemented with the Minimal Forbidden Tuple (MFT) approach is the fastest, while the Replace technique is promising for producing the smallest constrained covering arrays, especially for algorithms that construct test cases one-at-a-time. The results also show that there is an interplay between effectiveness of the constraint handler and the test suite generation algorithm into which it is developed