Peter B. Gibbons

Constructing test suites for interaction testing

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.

A variable strength interaction testing of components

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.

Facilities Layout Adjacency Determination: An Experimental Comparison of Three Graph Theoretic Heuristics

The facilities layout problem is concerned with laying out facilities on a planar site in order to design systems that are as efficient as possible. One approach to the problem involves the use of REL charts, which are tables that estimate the desirability of locating facilities next to each other, and the construction of a maximum weight planar graph that represents an efficient layout design. This method is not a complete one, however, since it specifies only which facilities are to be adjacent. Nevertheless, whenever the analyst has a great deal of freedom of design, it is a useful tool in the initial stages of laying out a new system. In this paper, we describe three graph theoretic heuristics that attempt to determine an optimal planar adjacency graph from a REL chart. Our computational experience suggests that these methods can provide effective solutions to problems of the size frequently encountered in practice by designers.

An algorithm for the steiner problem in graphs

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.

Construction methods for Bhaskar Rao and related designs

Mathematical and computational techniques are described for constructing and enumerating generalized Bhaskar Rao designs (GBRDs) . In particular, these methods are applied to GBRD(k + 1, k, 1(k − 1); G)s for 1 ≥ 1. Properties of the enumerated designs, such as automorphism groups, resolutions and contracted designs are tabulated. Also described are applications to group divisible designs, multi-dimensional Howell cubes, generalized Room squares, equidistant permutation arrays, and doubly resolvable two-fold triple systems.

Case studies and new results in combinatorial enumeration

A 1976 block design enumeration algorithm has been reimplemented with a number of enhancements. Its use is demonstrated with a number of case studies involving different kinds of incidence structures. New results include the enumeration of weakly union-free twofold triple systems of orders 12 and 13, Mendelsohn triple systems of orders 10 and 12, 2-(8, 4, 9), 2-(10, 4, 4), 2-(16, 4, 2), 3-(11, 5, 4) and 4-(12, 6, 4) block designs, and 2-(7, 3, λ) designs for 14 ≤ λ ≤ 16. Some of these results correct enumerations previously published in the literature. Additional results confirm independently produced results, some of which have been published quite recently.

A Census of Orthogonal Steiner Triple Systems of Order 15

Publisher Summary A Steiner triple system (STS) of order ν (STS(ν)) is a (ν,3,1)-balanced incomplete block design (BIBD). An STS (ν) is often represented by the pair ( V,B ) where V is the set of elements and B is the collection of blocks, or triples. Orthogonal STSs and the purpose of constructing Room squares are described in this chapter. The chapter presents the pairs of orthogonal STSs of orders 7, 13, and 19, conjecturing that such pairs exist for all orders. A brief survey of known results on orthogonal STSs is reviewed in the chapter. There exists only one pair of orthogonal STS (13)s. The chapter describes the existence of exactly 19 nonequivalent pairs of orthogonal STS (15)s involving 24 nonisomorphic systems.

The construction of antipodal triple systems by simulated annealing

Abstract An antipodal triple system of order v is a triple ( V , B , f ), where | V | = v , B is a set of cyclically oriented 3-subsets of V , and f : V → V is an involution with one fixed point such that: 1. (i) ( V , B ∪ f ( B )) is a Mendelsohn triple system. 2. (ii) B ∩ f ( B ) = 0. 3. (iii) f is an isomorphism between the Steiner triple system ( STS ) ( V , B ′) and the STS ( V , f ( B ′)), where B ′ is the same as B without orientation. 4. (iv) f preserves orientation. An STS (V,B) is hemispheric if there exists a cyclic orientation B ∗ of its block set B and an involution f such that (V,B ∗ , f) is an antipodal system. We use simulated annealing on a carefully chosen feasibility space to show that any STS(v) (V,B) , where 7 ⩽ v ⩽ 15, is hemispheric, and conjecture that this is true for any STS ( v ) v > 3. We were unable to find a way of applying the alternative computational techniques of hill climbing and backtracking to this problem.