Complete interaction testing of components is too costly in all but the smallest systems. Yet component interactions are likely to cause unexpected faults. Recently, design of experiment techniques have been applied to software testing to guarantee a minimum coverage of all t-way interactions across components. However, t is always fixed. This paper examines the need to vary the size of t in an individual test suite and defines a new object, the variable strength covering array that has this property. We present some computational methods to find variable strength arrays and provide initial bounds for a group of these objects.

Software system faults are often caused by unexpected interactions among components. Yet the size of a test suite required to test all possible combinations of interactions can be prohibitive in even a moderately sized project. Instead, we may use pairwise or t-way testing to provide a guarantee that all pairs or t-way combinations of components are tested together This concept draws on methods used in statistical testing for manufacturing and has been extended to software system testing. A covering array, CA(N; t, k, v), is an N/spl times/k array on v symbols such that every N x t sub-array contains all ordered subsets from v symbols of size t at least once. The properties of these objects, however do not necessarily satisfy real software testing needs. Instead we examine a less studied object, the mixed level covering array and propose a new object, the variable strength covering array, which provides a more robust environment for software interaction testing. Initial results are presented suggesting that heuristic search techniques are more effective than some of the known greedy methods for finding smaller sized test suites. We present a discussion of an integrated approach for finding covering arrays and discuss how application of these techniques can be used to construct variable strength arrays.

Abstract The Steiner problem in graphs is concerned with finding a set of edges with minimum total weight which connects a given subset of points in a weighted graph. A branch and bound algorithm for solving this problem is presented together with an interesting application to a problem in molecular evolution. Computational experience gained in using the algorithm compares favorably, for certain classes of graphs, with that of existing methods.