Problems and algorithms for covering arrays

Abstract

Covering arrays are combinatorial structures which extend the notion of orthogonal arrays and have applications in the realm of software testing. In this paper we raise several new problems motivated by these applications and discuss algorithms for their solution.

Constraint Models for the Covering Test Problem

“…Williams [32] describes a method, TConfig, for constructing covering arrays (for t ¼ 2) from smaller Fbuilding blocks,_ which is fast and was found to give better results than IPO (described below) except for heterogeneous alphabets, i.e., when g is not uniform for all parameters. Hartman and Raskin [16] describe their CTS (Combinatorial Test Services) package which aims to find small covering arrays, using a variety of constructive methods and choosing the best result. They also consider a number of related problems, such as maximising the number k of parameters with domains of size g in a t -wise covering test suite with a fixed number b of test cases, and finding a test suite giving maximum t-wise coverage from b tests.…”

“…The covering test problem is a direct application of the problem of covering arrays arising in hardware and software testing: the following definitions are based on Hartman and Raskin [16]. 1 Definition 1.…”

3-Way Software Testing with Budget Constraints

“…Because here we are looking to cover 80 3-way interactions but the total interactions covered is 74. These four choices of rows (1, 2, 3), (1,2,4), (1,3,4), (2,3,4) contain all eight possible values of the three parameters and remaining six choices contain only seven possible values of the three parameters. Given fixed values of n, k, and s, the covering arrays with budget constraints problem is to construct a covering array 3-CA(n, k, s) having large coverage measure µ.…”

“…There is a vast array of literature [1]- [3], [7], [8] on covering arrays, and the problem of determining the minimum size of covering arrays has been studied under many guises over the past thirty years. …”

CITLAB: A Laboratory for Combinatorial Interaction Testing

“…To describe a combinatorial problem would be sufficient to specify the number of variables and their cardinality. Many papers, like [17], simply use the exponential symbolic notation x y to model y parameters each of which can take x values. For heterogeneous alphabets, the notation is extended as x CITLAB language forces the designer to name parameters and to specify their types by listing all the values in their domain.…”