No abstract

Most existing work on t-way testing has focused on 2-way (or pairwise) testing, which aims to detect faults caused by interactions between any two parameters. However, faults can also be caused by interactions involving more than two parameters. In this paper, we generalize an existing strategy, called In-Parameter-Order (IPO), from pairwise testing to t-way testing. A major challenge of our generalization effort is dealing with the combinatorial growth in the number of combinations of parameter values. We describe a t-way testing tool, called FireEye, and discuss design decisions that are made to enable an efficient implementation of the generalized IPO strategy. We also report several experiments that are designed to evaluate the effectiveness of FireEye.

Abstract. A combinatorial form of Gram's relation for convex polytopes can be adapted for use in computing polytope volume. We present an algorithm for volume computation based on this observation. This algorithm is useful in finding the volume of a polytope given as the solution set of a system of linear inequalities, P = {x G R" : Ax < b} .As an illustration we compute a formula for the volume of a projective image of the «-cube. From this formula we deduce that, when A and b have rational entries (so that the volume of P is also a rational number), the number of binary digits in the denominator of the volume cannot be bounded by a polynomial in the total number of digits in the numerators and denominators of entries of A and b . This settles a question posed by Dyer and Frieze.

ABSTRACT. We discuss the linear independence of systems of m vectors in

Covering arrays are structures for well-representing extremely large input spaces and are used to efficiently implement blackbox testing for software and hardware. This paper proposes refinements over the In-Parameter-Order strategy (for arbitrary t). When constructing homogeneous-alphabet covering arrays, these refinements reduce runtime in nearly all cases by a factor of more than 5 and in some cases by factors as large as 280. This trend is increasing with the number of columns in the covering array. Moreover, the resulting covering arrays are about 5 % smaller. Consequently, this new algorithm has constructed many covering arrays that are the smallest in the literature. A heuristic variant of the algorithm sometimes produces comparably sized covering arrays while running significantly faster.