Covering arrays with mixed alphabet sizes

Moura, Lucia; Stardom, John; Stevens, Brett; Williams, Alan

doi:10.1002/jcd.10059

Cited by 51 publications

(29 citation statements)

References 27 publications

(50 reference statements)

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“…Let G and H be weighted graphs. A mapping φ from In the next proof, we use the concept of dropping the alphabet size of a particular column of a mixed covering array (from [11]). Let h ≥ g. To drop the alphabet size from h to g in a column of a covering array, we replace all symbols from Z h \Z g in the column by arbitrary symbols from Z g .…”

Section: Mixed Covering Arrays On Graphsmentioning

confidence: 99%

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Mixed covering arrays on graphs

Meagher

Moura

Zekaoui

2007

J of Combinatorial Designs

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Abstract:Covering arrays have applications in software, network and circuit testing. In this article, we consider a generalization of covering arrays that allows mixed alphabet sizes as well as a graph structure that specifies the pairwise interactions that need to be tested. Let k and n be positive integers, and let G be a graph with k vertices v 1 , v 2 , . . . , v k with respective vertex weights g 1 ≤ g 2 ≤ · · ·≤ g k . A mixed covering array on G, denoted by CA(n, G, k i=1 g i ), is an n × k array such that column i corresponds to v i , cells in column i are filled with elements from Z g i and every pair of columns i, j corresponding to an edge {v i , v j } in G has every possible pair from Z g i × Z g j appearing in some row. The number of rows in such array is called its size. Given a weighted graph G, a mixed covering array on G with minimum size is called optimal. In this article, we give upper and lower bounds on the size of mixed covering arrays on graphs based on graph homomorphisms. We provide constructions for covering arrays on graphs based on basic graph operations. In particular, we construct optimal mixed covering arrays on trees, cycles and bipartite graphs; the constructed optimal objects have the additional property of being nearly point balanced.

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Section: Mixed Covering Arrays On Graphsmentioning

confidence: 99%

“…This meets the requirement that different parameters in the system may take a different number of possible values. Constructions for mixed covering arrays are given in [5,11]. Another generalization of covering arrays are covering arrays on graphs.…”

Section: Introductionmentioning

confidence: 99%

Mixed covering arrays on graphs

Meagher

Moura

Zekaoui

2007

J of Combinatorial Designs

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“…TConfig constructs CAs using recursive functions that concatenate small CAs to create CAs with a larger number of columns. Moura et al (2003) introduced a set of recursive algorithms for constructing CAs based on CAs of small sizes. Some recursive methods are product constructions (Colbourn & Ling, 2009;Colbourn et al, 2006;Martirosyan & Colbourn, 2005).…”

Section: Relevant Related Workmentioning

confidence: 99%

Using Grid Computing for Constructing Ternary Covering Arrays

Ávila-George¹,

Torres-Jiménez²,

Carrión³

et al. 2012

Grid Computing - Technology and Applications, Widespread Coverage and New Horizons

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“…When used in testing, however, it is very unlikely that all configurable parameters will have the same number of levels. Mixed-level covering arrays [34,71] overcome this limitation by allowing the number of levels for each factor to be specified, which manifests in the actual array as each column having its own range of values while still maintaining the balance conditions.…”

Section: Contentsmentioning

confidence: 99%

“…Firstly, it is not often the case in real-world systems that the number of levels is uniform across all factors. Mixedlevel covering arrays, as proposed in [71], allow for factors to have different numbers of levels. We examine mixed-level variable strength covering arrays in greater detail in Section 3.3.…”

Section: Covering Arrays and Their Generalizationsmentioning

confidence: 99%

Variable strength covering arrays

Raaphorst

Moura

Stevens

2018

J of Combinatorial Designs

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Recently, covering arrays have been the subject of considerable research attention as they hold both theoretical interest and practical importance due to their applications to testing. In this thesis, we perform the first comprehensive study of a generalization of covering arrays called variable strength covering arrays, where we dictate the interactions to be covered in the array by modeling them as facets of an abstract simplicial complex.We outline the necessary background in the theory of hypergraphs, combinatorial testing, and design theory that is relevant to the study of variable strength covering arrays. We then approach questions that arise in variable strength covering arrays in a number of ways. We demonstrate their connections to hypergraph homomorphisms, and explore the properties of a particular family of abstract simplicial complexes, the qualitative independence hypergraphs. These hypergraphs are tightly linked to variable strength covering arrays, and we determine and identify several of their important properties and subhypergraphs.We give a detailed study of constructions for variable strength covering arrays, and provide several operations and divide-and-conquer techniques that can be used in building them. In addition, we give a construction using linear feedback shift registers from primitive polynomials of degree 3 over arbitrary finite fields to find variable strength covering arrays, which we extend to strength-3 covering arrays whose sizes are smaller than many of the best known sizes of covering arrays.We then give an algorithm for creating variable strength covering arrays over arbitrary abstract simplicial complexes, which builds the arrays one row at a time, using a density concept to guarantee that the size of the resultant array is asymptotic in the logarithm of the number of facets in the abstact simplicial complex. This algorithm is of immediate practical importance, as it can be used to create test suites for combinatorial testing.Finally, we use the Lovász Local Lemma to nonconstructively determine upper bounds on the sizes of arrays for a number of different families of hypergraphs. We lay out a framework that can be used for many hypergraphs, and then discuss possible strategies that can be taken in asymmetric problems.ii Acknowledgements This thesis certainly could not have been completed without the help of many people.Firstly and most importantly, I would like to extend my immeasurable thanks to both of my supervisors, Lucia Moura and Brett Stevens. As a lowly undergraduate student many years ago, I had the extreme fortune of being chosen to serve as a teaching assistant to work with Lucia Moura. I could never have predicted that that was to be the first step on a long and rewarding journey into academia. Through all the opportunities she gave me, I caught her infectious enthusiasm for research and had my eyes opened to the wonderful fields of design theory and covering arrays. Without her endless patience and compassion with my quirkiness, this thesis would never...

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Covering arrays with mixed alphabet sizes

Cited by 51 publications

References 27 publications

Mixed covering arrays on graphs

Mixed covering arrays on graphs

Using Grid Computing for Constructing Ternary Covering Arrays

Variable strength covering arrays

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