Peter B. Gibbons

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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(More)
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 -way interactions across components. However, is always fixed. This paper examines(More)
We describe various computing techniques for tackling chessboard domination problems and apply these to the determination of domination and irredundance numbers for queens’ and kings’ graphs. In particular we show that γ(Q15) = γ(Q16) = 9, confirm that γ(Q17) = γ(Q18) = 9, show that γ(Q19) = 10, show that i(Q18) = 10, improve the bound for i(Q19) to 10 ≤(More)
The Construction of Subsquare Free Latin Squares by Simulated Annealing J.R. Elliott and P.B. Gibbons Department of Computer Science University of Auckland New Zealand A simulated annealing algorithm is used in the construction of subsquare free Latin squares. The algorithm is described and experience from its application is reported. Results obtained(More)
Computing techniques are described which have resulted in the establishment of new results for the queens domination problem. In particular it is shown that the minimum cardinalities of independent sets of dominating queens for chessboards of size 14, 15, and 16 are 8, 9, and 9 respectively, and that the minimum cardinalities of sets of dominating queens(More)
The queens’ graph Qn has the squares of the n × n chessboard as its vertices, with two squares adjacent if they are in the same row, column, or diagonal. An irredundant set of queens has the property that each queen in the set attacks at least one square which is attacked by no other queen. IR(Qn) is the cardinality of the largest irredundant set of(More)
"We investigate<lb>of the all-ones matrix .]V for<lb>1) 16 over va,rious admissible groups. For 1) 16 all<lb>have been PIlumera,ted. For the case 7) 16 only some classes have been completely enumerated. Of particular<lb>are signings over the group since these can also<lb>be considHed as GDD(16 X 2,16,<lb>these over<lb>expanding,<lb>GDD(16 4,16,4)'s. We(More)
An antipodal triple system of order v is a triple (V, B, 1), where 1 V 1= 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: (i) (V, B U f(B)) is a Mendelsohn triple system. Oi) B n f(B) = 0. (iii) f is an isomorphism between the Steiner triple system (ST S) (V, B') and the STS (V,f(B')),(More)