Covering arrays with mixed alphabet sizes

Abstract

AbstractCovering arrays with mixed alphabet sizes, or simply mixed covering arrays, are natural generalizations of covering arrays that are motivated by applications in software and network testing. A (mixed) covering array A of type $\prod _{i=1}^{k}g_i$ is a k × N array with the cells of row i filled with elements from ℤ and having the property that for every two rows i and j and every ordered pair of elements (e,f) ∈ ℤ × ℤ, there exists at least one column c, 1 ≤ c ≤ N, such that Ai,c = e and Aj,c = f. The (mixed) covering array number, denoted by $ca(\prod _{i=1}^{k}g_i)$, is the minimum N for which a covering array of type $\prod _{i=1}^{k}g_i$ with N columns exists. In this paper, several constructions for mixed covering arrays are presented, and the mixed covering array numbers are determined for nearly all cases with k = 4 and for a number of cases with k = 5. © 2003 Wiley Periodicals, Inc. J Combin Designs 11: 413–432, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jcd.10059