A simple lower bound on edge coverings by cliques
Discrete Mathematics
Model-based testing in practice
Proceedings of the 21st international conference on Software engineering
On the hardness of approximating minimization problems
Journal of the ACM (JACM)
Covering edges by cliques with regard to keyword conflicts and intersection graphs
Communications of the ACM
An Investigation of the Applicability of Design of Experiments to Software Testing
SEW '02 Proceedings of the 27th Annual NASA Goddard Software Engineering Workshop (SEW-27'02)
A Measure for Component Interaction Test Coverage
AICCSA '01 Proceedings of the ACS/IEEE International Conference on Computer Systems and Applications
Software Fault Interactions and Implications for Software Testing
IEEE Transactions on Software Engineering
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Handbook of Combinatorial Designs, Second Edition (Discrete Mathematics and Its Applications)
Interaction testing of highly-configurable systems in the presence of constraints
Proceedings of the 2007 international symposium on Software testing and analysis
Covering arrays avoiding forbidden edges
Theoretical Computer Science
Locating Errors Using ELAs, Covering Arrays, and Adaptive Testing Algorithms
SIAM Journal on Discrete Mathematics
Hardness results for covering arrays avoiding forbidden edges and error-locating arrays
Theoretical Computer Science
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In this paper, we look at covering arrays with forbidden edges (CAFEs), which are used in testing applications (software, networks, circuits, drug interaction, material mixtures, etc.) where certain combinations of parameter values are forbidden. Covering arrays are classical objects used in these applications, but the situation of dealing with forbidden configurations is much less studied. Danziger et. al. [8] have recently studied this problem and shown some computational complexity results, but left some important open questions. Around the same time, Martinez et al. [18] defined and studied error-locating arrays (ELAs), which are very related to CAFEs, leaving similar computational complexity questions. In particular, these papers showed polynomial-time solvability of the existence of CAFEs and ELAs for binary alphabets (g=2), and the NP-hardness of these problems for g≥5. This not only left open the complexity of determining optimum CAFEs and ELAs for g=2,3,4, but some suspicion that the binary case might be solved by a polynomial-time algorithm. In this paper, we prove that optimizing CAFEs and ELAs is indeed NP-hard even when restricted to the case of binary alphabets. We also provide a hardness of approximation result. The proof strategy uses a reduction from edge clique covers of graphs (ECCs) and covers all cases of g. We also explore important relationships between ECCs and CAFEs and give some new bounds for uniform ECCs and CAFEs.