Given a set S of v ≥ 2 symbols, and integers k ≥ t ≥ 2 and N ≥ 1, an N × k array A ∈ SN×k is an (N ; t, k, v)-covering array if all sequences in S appear as rows in every N × t subarray of A. These arrays have a wide variety of applications, driving the search for small covering arrays. The covering array number, CAN(t, k, v), is the smallest N for which an (N ; t, k, v)-covering array exists. ...

The construction of covering arrays with the fewest rows remains a challenging problem. Most computational and recursive constructions result in extensive repetition of coverage. While some is necessary, some is not. By reducing the repeated coverage, metaheuristic search techniques typically outperform simpler computational methods, but they have been applied in a limited set of cases. Time co...

Recent research activities have demonstrated the effective application of combinatorial optimization in different areas, especially in software testing. Covering array (CA) has been introduced as a representation of the combinations in one complete set. CAλ(N; t, k, v) is an N × k array in which each t-tuple for an N × t sub array occurs at least λ times, where t is the combination strength, k ...

ARTICLE INFO Covering arrays of strength two have been widely studied as combinatorial models of software interaction test suites for pairwise testing. While numerous algorithmic techniques have been developed for the generation of covering arrays with few columns (factors), the construction of covering arrays with many factors and few tests by these techniques is problematic. Random generation...

A covering array t-CAðn; k; gÞ is a k n array on a set of g symbols with the property that in each t n subarray, every t 1 column appears at least once. This paper improves many of the best known upper bounds on n for covering arrays, 2-CAðn; k; gÞ with gþ 1 k 2g, for g 1⁄4 3 12 by a construction which in many of these cases produces a 2-CAðn; k; gÞ with n 1⁄4 kðg 1Þ þ 1. The construction is an...

A t − α covering array is an m × n matrix, with entries from an alphabet of size α, such that for any choice of t rows, and any ordered string of t letters of the alphabet, there exists a column such that the “values” of the rows in that column match those of the string of letters. We use the Lovász Local Lemma in conjunction with a new tiling-based probability model to improve the upper bound ...

A ternary covering array (CA(N ; t, k, 3)) is an N × k array with entries from the set {0, 1, 2} where every N × t subarray contains each of the 3 combinations at least once. Here, t is called the strength, k the degree or number of factors, and the alphabet is set to 3. Covering arrays (CAs) are combinatorial designs that have applications in experimental designs and they have been proved to b...

Many researchers have been working on the greedy algorithms for covering array generation; a framework has been built to integrate most of these greedy methods, and more new approaches can be derived from this framework. However, such a framework is affected by multiple dependent or independent factors, which makes its deployment and optimization very challenging. In this paper, we design Hill ...

Recursive constructions for covering arrays employ small ingredient covering arrays to build large ones. At present the most effective methods are “cut–and–paste” (or Roux-type) and column replacement techniques. Both can introduce substantial duplication of coverage; if unnecessary duplication can be avoided then the recursion can yield a smaller array. Two extensions of covering arrays are in...