Alan C. H. Ling

Constructing strength three covering arrays with augmented annealing

A covering arrayCA(N;t,k,v) is an Nxk array such that every Nxt sub-array contains all t-tuples from v symbols at least once, where t is the strength of the array. One application of these objects is to generate software test suites to cover all t-sets of component interactions. Methods for construction of covering arrays for software testing have focused on two main areas. The first is finding new algebraic and combinatorial constructions that produce smaller covering arrays. The second is refining computational search algorithms to find smaller covering arrays more quickly. In this paper, we examine some new cut-and-paste techniques for strength three covering arrays that combine recursive combinatorial constructions with computational search; when simulated annealing is the base method, this is augmented annealing. This method leverages the computational efficiency and optimality of size obtained through combinatorial constructions while benefiting from the generality of a heuristic search. We present a few examples of specific constructions and provide new bounds for some strength three covering arrays.

Augmenting simulated annealing to build interaction test suites

Component based software development is prone to unexpected interaction faults. The goal is to test as many-potential interactions as is feasible within time and budget constraints. Two combinatorial objects, the orthogonal array and the covering array, can be used to generate test suites that provide a guarantee for coverage of all t-sets of component interactions in the case when the testing of all interactions is not possible. Methods for construction of these types of test suites have focused on two main areas. The first is finding new algebraic constructions that produce smaller test suites. The second is refining computational search algorithms to find smaller test suites more quickly. In this paper we explore one method for constructing covering arrays of strength three that combines algebraic constructions with computational search. This method leverages the computational efficiency and optimality of size obtained through algebraic constructions while benefiting from the generality of a heuristic search. We present a few examples of specific constructions and provide some new bounds for some strength three covering arrays.

Permutation arrays for powerline communication and mutually orthogonal latin squares

We develop a connection between permutation arrays that are used in powerline communication and well-studied combinatorial objects, mutually orthogonal latin squares (MOLS). From this connection, many new results on permutation arrays can be obtained.

Group divisible designs with block size four and group type gum1 for small g

Abstract Non-uniform group divisible designs are instrumental in the constructions for other types of designs. Most of the progress for the existence of { 4 } -GDDs of type g u m 1 is on the case when g u is even, where the existence for small g has played a key role. In order to determine the spectrum for { 4 } -GDDs of type g u m 1 with g u being odd, we continue to investigate the small cases with g ∈ { 7 , 9 , 21 } in this paper. We show that, for each g ∈ { 7 , 9 , 21 } , the necessary conditions for the existence of a { 4 } -GDD of type g u m 1 are also sufficient. As the applications of these GDDs, we obtain a few pairwise balanced designs with minimum block size 4. Meanwhile, we also improve the existence result for frame self-orthogonal Mendelsohn triple systems of type h n by reducing an infinite class of possible exceptions, namely n = 9 and h ≡ 2 mod 6 , to eight undetermined cases.

Construction techniques for anti-pasch steiner triple systems

Four methods for constructing anti-Pasch Steiner triple systems are developed. The first generalises a construction of Stinson and Wei to obtain a general singular direct product construction. The second generalises the Bose construction. The third employs a construction due to Lu. The fourth employs Wilson-type inflation techniques using Latin squares having no subsquares of order two. As a consequence of these constructions we are able to produce anti-Pasch systems of order

Pairwise Balanced Designs with Consecutive Block Sizes

v

A class of partial triple systems with applications in survey sampling

for

Asymptotically optimal erasure-resilient codes for large disk arrays

v\equiv 1

Modified group divisible designs with block size four

or

The Existence of Kirkman Squares—Doubly Resolvable ( v ,3,1)- BIBD s

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